\index{a"|b} is broken but \index{a"@b}, \index{a""b}, \index{a"!b} all work

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{makeidx}


\usepackage{hyperref}

\makeindex

\begin{document}


% \index{a"|b}% error if this is uncommented

\index{a"@b}
\index{a""b}
\index{a"!b}

\printindex
\end{document}

But with the commented line uncommented:

! Argument of \T1\b has an extra }.
<inserted text> 
                \par 
l.6   \item a|hyperindexformat{\b}
                                  , 1
!  ==> Fatal error occurred, no output PDF file produced!
Transcript written on testindexhyperref.log.

Procedure:

pdflatex --halt-on-error testindexhyperref
makeindex testindexhyperref
pdflatex --halt-on-error testindexhyperref

I did check hyperref documentation but found nothing on this.

Start with the minimal LaTeX example in testindexhyperref and reproduce it using pdflatex, makeindex, and pdflatex as listed. Compare the failing \index{a"|b} case with the working @, "", and ! variants; done means the pipe variant completes without the reported T1\b error and produces the index.