Printing "ibid" for biblatex-chicago authordate style

Question

I'm using the authordate style under biblatex-chicago. However, due to specific assignment requirements, I need to include my citations inside footnotes.

While I have no problem doing this by using \footcite, consecutive references to the same source simply print the page number under the footnote and nothing else.

While I understand that this is the correct method according to the CMOS inline citation style, because I am using footnotes, I need an "Ibid." to be printed in the front, while still retaining the simple author-year citation style.

I don't want to use the notes option where the full citation with title and publisher etc. appears (I just want the author and year to appear in the footnote), and I specifically want to use biblatex-chicago instead of biblatex. How can I achieve this, through the customisation of styles or otherwise?

MWE:

\documentclass{article}
\usepackage[authordate,backend=biber]{biblatex-chicago}
\bibliography{references}

\begin{filecontents}{references.bib}
    @book{book,
        title={Reference},
        author={Yamada, Taro},
        year={2001},
    }
\end{filecontents}

\begin{document}
    First citation\footcite[123-124]{book}.
    Second citation\footcite[150]{book}.
\end{document}

Actual output:

Expected output:

Answer 1

We can redefine \footcite specifically to write "ibid." with

\DeclareCiteCommand{\footcite}[\mkbibfootnote]
  {\renewbibmacro*{cite:ibid}{\printtext[bibhyperref]{\bibstring[\mkibid]{ibidem}}}%
   \usebibmacro{cite:init}%
   \usebibmacro{prenote}}
  {\usebibmacro{citeindex}%
   \usebibmacro{cite}}
  {}%\multicitedelim
  {\usebibmacro{postnote}}

The MWE

\documentclass{article}
\usepackage[authordate,backend=biber,isbn=false]{biblatex-chicago}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
    @book{book,
        title={Reference},
        author={Yamada, Taro},
        year={2001},
    }
\end{filecontents}
\bibliography{\jobname}


\DeclareCiteCommand{\footcite}[\mkbibfootnote]
  {\renewbibmacro*{cite:ibid}{\printtext[bibhyperref]{\bibstring[\mkibid]{ibidem}}}%
   \usebibmacro{cite:init}%
   \usebibmacro{prenote}}
  {\usebibmacro{citeindex}%
   \usebibmacro{cite}}
  {}%\multicitedelim
  {\usebibmacro{postnote}}

\begin{document}
    First citation\footcite[123-124]{book}.
    Second citation\footcite[150]{book}.
\end{document}

then gives the expected output

---

If you want this globally, i.e. for all \*cite commands go with the one-liner

\renewbibmacro*{cite:ibid}{\printtext[bibhyperref]{\bibstring[\mkibid]{ibidem}}}

instead.