How to hide customized header on section start

Question

This question is directly related to this one. I used the code and wanted to have an empty pagestyle on pages having a section start and at the same time the header should be customized like this one. When I use the codes together it won't work anymore, because the title in the header is now the title from the table of contents.

When a section starts there is no header:

When a section starts and has another [sub]section in it there should be a header but is not.

When there is no section at the page the header should have the rightmark if it's not blank, else the leftmark. That worked before merging the codes, now it doesn't (in this example it should be the current section):

Here are some cases for what should be inside the header and when there should be a header:

• If the page starts with a section and has no previous text that breaked to the page there shouldn't be a header.
• If there is text that breaks to the page from a [*]section there should be a header containing the number and title of [*].
• If the page doesn't has breaking text and starts with a sub[*]section it should have a header and in the header the number and title of the upper section e.g. if the page starts a subsection it should hold the section title.

How can I get both working, no header at section start and a customized header on pages, which don't have a section start or have [sub]sections which break to this page?

Here is a MWE:

\documentclass[12pt,a4paper,ngerman]{article}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\hypersetup{breaklinks=true,
            pdfborder={0 0 0},
            ngerman}
\usepackage{times}
\usepackage{microtype}
\usepackage[parfill]{parskip}

\usepackage[
    a4paper,
    left=4cm,
    right=3cm,
    top=3cm,
    bottom=3cm,
    %showframe,
    headheight=15pt,
    includeheadfoot
]{geometry}
\linespread{1.25}

\usepackage{blindtext}

\renewcommand{\sfdefault}{\rmdefault}

\usepackage{fancyhdr}
\usepackage{chngcntr}
\usepackage{xparse}
\fancyhf{}
\lhead{\nouppercase{\rightorleftmark}}
\cfoot{\thepage}

\fancypagestyle{section}{%
  \fancyhf{}%
  \fancyfoot[C]{\thepage}
  \renewcommand{\headrulewidth}{0pt}
}

\counterwithin{figure}{section}
\counterwithin{table}{section}

% https://tex.stackexchange.com/a/187853/49121
\let\originalsection\section
\RenewDocumentCommand{\section}{som}{%
  \IfBooleanTF{#1}
    {\originalsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsection{#3}}
      {\originalsection[#2]{#3}}%
    }%
  \thispagestyle{section}%
}

%https://tex.stackexchange.com/a/101926/49121
\makeatletter
\newcommand{\rightorleftmark}{%
  \begingroup\protected@edef\x{\rightmark}%
  \ifx\x\@empty
    \endgroup\leftmark
  \else
    \endgroup\rightmark
  \fi}
\makeatother

\begin{document}
  \pagestyle{plain}
  \pagenumbering{Roman}
  \setcounter{page}{1} % when using custom titlepage

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Inhaltsverzeichnis}{tableofcontents}
  \markboth{Inhaltsverzeichnis}{}
  \tableofcontents

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Abbildungsverzeichnis}{listoffigures}
  \listoffigures

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Tabellenverzeichnis}{listoftables}
  \listoftables


  \cleardoublepage
  \phantomsection
  \pagenumbering{arabic}
  \pagestyle{fancy}
  \cleardoublepage
  \blinddocument

\end{document}

Answer 1

Here is a solution for the real original problem, including the third requirement (text header of next higher (*)section command if the page starts with a sub(*)section. I don't know if it covers all corner cases, but the normal cases seem to work well. I have put this as a separate answer because both address slightly different problems.

\documentclass[12pt,a4paper,ngerman]{article}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\hypersetup{breaklinks=true,
            pdfborder={0 0 0},
            ngerman}
\usepackage{times}
\usepackage{microtype}
\usepackage[parfill]{parskip}

\usepackage[
    a4paper,
    left=4cm,
    right=3cm,
    top=3cm,
    bottom=2.9cm,
    %showframe,
    headheight=15pt,
    includeheadfoot
]{geometry}
\linespread{1.25}

\usepackage{blindtext}

\renewcommand{\sfdefault}{\rmdefault}

\usepackage{chngcntr}

\counterwithin{figure}{section}
\counterwithin{table}{section}

\usepackage{xparse}
\usepackage{ifthen}
\usepackage{extramarks}

\usepackage{fancyhdr}
\pagestyle{fancy} % give \pagestyle{fancy} here to initialize fancyhdr.
\fancyhf{}

% We are going to use \rightmark for the section or subsection title to be
% placed in the header and \firstleftmark (from the extramarks package)
% to indicate where it comes from:
% prev = from a (sub)section on the previous page
% newpage = from a \newpage command 
% section = from a \section command on this page
% subsection = from a \subsection command on this page
% We use \firstleftmark because the normal \leftmark gives us the LAST
% left mark on the page instead of the first one.
%
% Our solution is to issue a \markboth command with "prev" as left part
% before each \(sub)section command. This serves two purposes:
% (1) In this way the previous (sub)section title will be used in the header.
% (2) When the pagebreak comes just before the \section command, the
% previous page will have a "prev" (last) \leftmark and the current page
% will have a "section" \firstleftmark. This combination determines that
% there is a section at the top of the page.
% In order to work properly, \newpage must also issue such a mark. In
% that case we put "newpage" in the leftmark, but that information is
% currently not used.

% Test if there is a section at the top of the page.

\newcommand{\iftopsection}[2]{% %1 = true action, #2 = false action
     \ifthenelse{\equal{\firstleftmark}{section}}{#1}{#2}}

% If there is a section on top of the page, suppress the header
% If it is a subsection, use the last section title (in \firstleftxmark)
% If it is a subsubsection, use the last subsection title (in \firstrightxmark).
% Otherwise we have overflow from the previous page and we use \rightmark
% (which should be the current (*)section from \prevmark).

\lhead{\nouppercase{%
     \iftopsection{}
       {\ifthenelse{\equal{\firstleftmark}{subsection}}
         {\firstleftxmark}%
         {\ifthenelse{\equal{\firstleftmark}{subsubsection}}
           {\firstrightxmark}{\rightmark}}}}}

%% \rhead{\firstleftmark} % This is for debugging!!!!!
\cfoot{\thepage}

% If there is a \section command on the top of the page, make \headrule empty.

\let\originalheadrule\headrule
\renewcommand{\headrule}{%
     \iftopsection{}{\originalheadrule}}

% Define the format the (*)section titles have in the header

\newcommand{\secTH}[1]{\thesection\quad #1}
\newcommand{\subsecTH}[1]{\thesubsection\quad #1}
\newcommand{\subsubsecTH}[1]{\thesubsubsection\quad #1}

% Mark commands for the (*)sections. We set the title in the rightmark,
% and also keep the extramarks current (last section and subsection title).

\renewcommand{\sectionmark}[1]{\markboth{section}{\secTH{#1}}%
   \extramarks{\secTH{#1}}{}}
\renewcommand{\subsectionmark}[1]{\markboth{subsection}{\subsecTH{#1}}%
  \extramarks{\prevsection}{\subsecTH{#1}}}
\renewcommand{\subsubsectionmark}[1]{\markboth{subsubsection}{\subsubsecTH{#1}}}

% We remember the title of the previous (*)section in \prevmark.
% We have also commands to remember the last section and subsection
% titles specifically. We will remember these with \extramarks.

\newcommand{\prevmark}{}
\newcommand{\prevsection}{}
\newcommand{\prevsubsection}{}

% This inserts the \prevmark as a mark before the (sub)section command.
% There is a \nopagebreak before it, so that (hopefully) it will stick
% with the previous text. So we hope the page will be broken after it if necessary.
% And then we set the new \prevmark value to the (sub)section title.
% We set the last section and subsection titles with \extramarks.

\newcommand{\insertprevmark}[1]{%
  \nopagebreak
  \ifx\prevmark\empty\else\markboth{prev}{\prevmark}%
  \extramarks{\prevsection}{\prevsubsection}\fi
  \renewcommand{\prevmark}{#1}%
}

% Change \section so that it will insert a "prev" mark first. 
% http://tex.stackexchange.com/a/187853/49121
\let\originalsection\section
\RenewDocumentCommand{\section}{som}{%
  \insertprevmark{\secTH{#3}}%
  \renewcommand{\prevsection}{\secTH{#3}}%
  \renewcommand{\prevsubsection}{}%
  \IfBooleanTF{#1}
    {\originalsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsection{#3}}
      {\originalsection[#2]{#3}}%
    }%
}

% Change \subsection so that it will insert a "prev" mark first. 
\let\originalsubsection\subsection
\RenewDocumentCommand{\subsection}{som}{%
  \insertprevmark{\subsecTH{#3}}%
  \renewcommand{\prevsubsection}{\subsecTH{#3}}%
  \IfBooleanTF{#1}
    {\originalsubsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsubsection{#3}}
      {\originalsubsection[#2]{#3}}%
    }%
}

% Change \subsubsection so that it will insert a "prev" mark first. 
\let\originalsubsubsection\subsubsection
\RenewDocumentCommand{\subsubsection}{som}{%
  \insertprevmark{\subsubsecTH{#3}}%
  \IfBooleanTF{#1}
    {\originalsubsubsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsubsubsection{#3}}
      {\originalsubsubsection[#2]{#3}}%
    }%
}

% adapt \newpage so that it issues a "prev" mark, and makes \prevmark empty

\let\originalnewpage\newpage
\renewcommand{\newpage}{\markboth{newpage}{\prevmark}\global\let\prevmark\empty\originalnewpage}

\begin{document}
  \pagestyle{plain}
  \pagenumbering{Roman}
  \setcounter{page}{1} % when using custom titlepage

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Inhaltsverzeichnis}{tableofcontents}
  \markboth{Inhaltsverzeichnis}{}
  \tableofcontents

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Abbildungsverzeichnis}{listoffigures}
  \listoffigures

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Tabellenverzeichnis}{listoftables}
  \listoftables

  \cleardoublepage
  \phantomsection
  \pagenumbering{arabic}
  \pagestyle{fancy}
  \section{This is a test section}
  \blindtext
  \subsection{This is a subsection}
  \blindtext
  \section{This is another section}


This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   

\subsection{This is another subsection}

  Some more text. 

 \cleardoublepage
  \blinddocument

\end{document}

Answer 2

Original answer: Instead of testing if the \rightmark is empty and then choosing \leftmark it is much easier to make sure that when the \leftmark is set, also the \rightmark is set to the same value.

This can be done with:

\renewcommand{\sectionmark}[1]{\markboth{\thesection. #1}{\thesection. #1}}

and the you can just use \rightmark:

\lhead{\nouppercase{\rightmark}}

Edit: Below I have added what I think is a complete solution to the original problem.

Change Note Dec 20,2016: I have replaced the solution with a simpler one, that does not need \topmark. I think it is more robust.

However the OP brought to my attention that it doesn't satisfy the third requirement:

• If the page doesn't has breaking text and starts with a sub[*]section it should have a header and in the header the number and title of the upper section e.g. if the page starts a subsection it should hold the section title.

Instead on a page that starts with a sub[*]section it uses the title of that sub[*]section in the header. I am working to find a solution to the other requirement.

Now here is a solution to the original (complicated) problem. It's quite some trickery with marks, and I hope I have covered all the corner cases. Explanation is in the comments.

\documentclass[12pt,a4paper,ngerman]{article}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\hypersetup{breaklinks=true,
            pdfborder={0 0 0},
            ngerman}
\usepackage{times}
\usepackage{microtype}
\usepackage[parfill]{parskip}

\usepackage[
    a4paper,
    left=4cm,
    right=3cm,
    top=3cm,
    bottom=3cm,
    %showframe,
    headheight=15pt,
    includeheadfoot
]{geometry}
\linespread{1.25}

\usepackage{blindtext}

\renewcommand{\sfdefault}{\rmdefault}

\usepackage{chngcntr}

\counterwithin{figure}{section}
\counterwithin{table}{section}

\usepackage{xparse}
\usepackage{ifthen}
\usepackage{extramarks}

\usepackage{fancyhdr}
\pagestyle{fancy} % give \pagestyle{fancy} here to initialize fancyhdr.
\fancyhf{}

% We are going to use \rightmark for the section or subsection title to be
% placed in the header and \firstleftmark (from the extramarks package)
% to indicate where it comes from:
% prev = from a (sub)section on the previous page
% section = from a \section command on this page
% subsection = from a \subsection command on this page
% We use \firstleftmark because the normal \leftmark gives us the LAST
% left mark on the page instead of the first one.
%
% Our solution is to issue a \markboth command with "prev" as left part
% before each \(sub)section command. This serves two purposes:
% (1) In this way the previous (sub)section title will be used in the header.
% (2) When the pagebreak comes just before the \section command, the
% previous page will have a "prev" (last) \leftmark and the current page
% will have a "section" \firstleftmark. This combination determines that
% there is a section at the top of the page. In order to work properly,
% a \newpage must also issue such a mark.

% If there is a section command at the top, don't put a header (put an
% empty header)

% Test if there is a section at the top of the page.

\newcommand{\iftopsection}[2]{% %1 = true action, #2 = false action
     \ifthenelse{\equal{\firstleftmark}{section}}{#1}{#2}}

\lhead{\nouppercase{%
     \iftopsection{}{\rightmark}}}
%\rhead{\firstleftmark} % This is for debugging!!!!!
\cfoot{\thepage}

% If there is a \section command on the top of the page, make \headrule empty.

\let\originalheadrule\headrule
\renewcommand{\headrule}{%
     \iftopsection{}{\originalheadrule}}

\renewcommand{\sectionmark}[1]{\markboth{section}{\thesection\ #1}}
\renewcommand{\subsectionmark}[1]{\markboth{subsection}{\thesubsection\ #1}}

% We remember the title of the previous (sub)section in \prevmark.

\newcommand{\prevmark}{}
% This inserts the \prevmark as a mark before the (sub)section command.
% There is a \nopagebreak before it, so that (hopefully) it will stick
% with the previous text. So we hope the page will be broken after it if necessary.
% And then we set the new \prevmark value to the (sub)section title.

\newcommand{\insertprevmark}[1]{%
  \nopagebreak
  \ifx\prevmark\empty\else\markboth{prev}{\prevmark}\fi
  \renewcommand{\prevmark}{#1}%
}

% Change \section so that it will insert a "prev" mark first. 
% http://tex.stackexchange.com/a/187853/49121
\let\originalsection\section
\RenewDocumentCommand{\section}{som}{%
  \insertprevmark{\thesection\ #3}%
  \IfBooleanTF{#1}
    {\originalsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsection{#3}}
      {\originalsection[#2]{#3}}%
    }%
}

% Change \subsection so that it will insert a "prev" mark first. 
\let\originalsubsection\subsection
\RenewDocumentCommand{\subsection}{som}{%
  \insertprevmark{\thesubsection\ #3}%
  \IfBooleanTF{#1}
    {\originalsubsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsubsection{#3}}
      {\originalsubsection[#2]{#3}}%
    }%
}

% Change \subsubsection so that it will insert a "prev" mark first. 
\let\originalsubsubsection\subsubsection
\RenewDocumentCommand{\subsubsection}{som}{%
  \insertprevmark{\thesubsubsection\ #3}%
  \IfBooleanTF{#1}
    {\originalsubsubsection*{#3}}
    {\IfNoValueTF{#2}
      {\originalsubsubsection{#3}}
      {\originalsubsubsection[#2]{#3}}%
    }%
}

% adapt \newpage so that it issues a "prev" mark, and makes \prevmark empty

\let\originalnewpage\newpage
\renewcommand{\newpage}{\markboth{prev}{\prevmark}\global\let\prevmark\empty\originalnewpage}

\begin{document}
  \pagestyle{plain}
  \pagenumbering{Roman}
  \setcounter{page}{1} % when using custom titlepage

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Inhaltsverzeichnis}{tableofcontents}
  \markboth{Inhaltsverzeichnis}{}
  \tableofcontents

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Abbildungsverzeichnis}{listoffigures}
  \listoffigures

  \cleardoublepage
  \phantomsection
  \pdfbookmark{Tabellenverzeichnis}{listoftables}
  \listoftables

  \cleardoublepage
  \phantomsection
  \pagenumbering{arabic}
  \pagestyle{fancy}
  \section{This is a test section}
  \blindtext
  \subsection{This is a subsection}
  \blindtext
  \section{This is another section}


This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   
This is some text.   This is some text.   This is some text.   

Comment out these two lines so that the next subsection starts at the top
of the page. Then the header will become that subsection title.

  \subsection{This is another subsection}
  Some more text. 

 \cleardoublepage
  \blinddocument

\end{document}