When is TeX in “no mode”?

Question

TeX can be in 7 distinct modes:

1. Vertical mode: this is the mode in which TeX starts, and build pages.
2. Internal vertical mode: TeX is in this mode within \vbox{...}.
3. Horizontal mode: when constructing paragraphs.
4. Restricted horizontal mode: within an \hbox{...}.
5. Display math mode: $$...$$ (and LaTeX's other display math environments).
6. Math mode: $...$ for inline math.
7. No mode: only within \write commands?

The existence of the no mode mode can be ascertained by running

\tracingall
\immediate\write16{\iftrue\fi}
\end

(with the plain TeX format). The log contains

 \write->\iftrue \fi 
 {no mode: \iftrue: (level 1)}
 {true}
 {\fi: \iftrue (level 1)}

 {vertical mode: blank space  }
 {\end}

As you can see, TeX writes down the mode for the first command run in that mode. In this snippet, we can see no mode and vertical mode.

So far, I noted that neither \message nor \special change the mode to no mode. Only \write seems to do it.

Answer 1

no mode in tex.web corresponds to the variable modehaving the value 0. This can be seen in the procedure print_mode (§211), i.e.,

else if m=0 then print("no")

Now the only place in TeX where this variable is set to zero is in §1371 which is the code that expands a \write statement.

So the answer to your question is: yes that is the only place.