Answer by simplifying the code preamble code (but making more difficult the user usage) after OP's request:
You could replace your \renewcommand{\sectionmark}[1]{\markright{#1}}
by \renewcommand{\sectionmark}[1]{\gdef\rightmark{#1}}
\documentclass[10pt]{book}
\usepackage[nobottomtitles]{titlesec}
\usepackage{kantlipsum}
\usepackage{fancyhdr}
\makeatletter%hier definition schriftgrößen-makro
\newcommand\chapsize{\@setfontsize\chapsize{13pt}{6}}
\newcommand\secsize{\@setfontsize\secsize{11.5pt}{6}}
\newcommand\pnsize{\@setfontsize\pnsize{10.5pt}{6}}
\newcommand\appsize{\@setfontsize\appsize{9pt}{6}}
\makeatother
\titleformat{\chapter}[hang]
{\chapsize\centering}{\thechapter.\ }{0pt}{}
\titleformat{\section}[hang]
{\secsize\centering}{\thesection\ }{0pt}{}
\titlespacing*{\chapter}{0pt}{0pt}{8mm}
\titlespacing*{\section}{0pt}{24pt}{4.233mm}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\sectionmark}[1]{\gdef\rightmark{#1}}
\fancyhf{}
\fancyfoot[LE,RO]{\pnsize{\thepage}}
\fancyhead[CO]{\fontsize{9.5}{10.5}\selectfont\scshape\MakeLowercase{\rightmark}}
\fancyhead[CE]{\fontsize{9.5}{10.5}\selectfont\scshape\MakeLowercase{\leftmark}}
\renewcommand{\headrulewidth}{0pt}
\begin{document}
\chapter{Chapter One}
\section{First Section}
\kant[1-7]
\section{Second section: Too much text for a running head}
\sectionmark{Second section}
\kant[8-15]
\end{document}
Old answer: Automating (adding in the definition of \section a \sectionmark command )
You could redefine section according to my post here to have an extra ability of using a "starred" section but with optional argument that would mean it will be a normal (non starred) section with changed \sectionmark .
See how it works below in your changed MWE:
\documentclass[10pt]{book}
\usepackage[nobottomtitles]{titlesec}
\usepackage{kantlipsum}
\usepackage{fancyhdr}
\makeatletter%hier definition schriftgrößen-makro
\newcommand\chapsize{\@setfontsize\chapsize{13pt}{6}}
\newcommand\secsize{\@setfontsize\secsize{11.5pt}{6}}
\newcommand\pnsize{\@setfontsize\pnsize{10.5pt}{6}}
\newcommand\appsize{\@setfontsize\appsize{9pt}{6}}
\makeatother
\titleformat{\chapter}[hang]
{\chapsize\centering}{\thechapter.\ }{0pt}{}
\titleformat{\section}[hang]
{\secsize\centering}{\thesection\ }{0pt}{}
\titlespacing*{\chapter}{0pt}{0pt}{8mm}
\titlespacing*{\section}{0pt}{24pt}{4.233mm}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\sectionmark}[1]{\gdef\rightmark{#1}}
\fancyhf{}
\fancyfoot[LE,RO]{\pnsize{\thepage}}
\fancyhead[CO]{\fontsize{9.5}{10.5}\selectfont\scshape\MakeLowercase{\rightmark}}
\fancyhead[CE]{\fontsize{9.5}{10.5}\selectfont\scshape\MakeLowercase{\leftmark}}
\renewcommand{\headrulewidth}{0pt}
\let\oldsection\section
\makeatletter
\def\section{%
\@ifstar{\@Starred}{\@nonStarred}%
}
\def\@Starred{%
\@ifnextchar[%
{\GenericWarning{}{Warning: A starred section can not have optional parameters. I am going to ignore them!}\@StarredWith}%
{\@StarredWithout}%
}
\def\@StarredWith[#1]#2{%%
\oldsection{#2}\sectionmark{#1}%
}
\def\@StarredWithout#1{%
\oldsection*{#1}%
}
\def\@nonStarred{%
\@ifnextchar[%
{\@nonStarredWith}%
{\@nonStarredWithout}%
}
\def\@nonStarredWith[#1]#2{%
\oldsection[#1]{#2}%
}
\def\@nonStarredWithout#1{%
\oldsection{#1}%
}
\makeatother
\begin{document}
\chapter{Chapter One}
\section{First Section}
\kant[1-7]
\section*[Second section]{Second section: Too much text for a running head}
\kant[8-15]
\end{document}
\chaptercontains a command\thispagestyle{plain}. Biside this, you should not use 'sectionmark this way, bu use the optional argument of\sectionlike in\section[Short enough]{Second section: Too much text for a running head}` – Jhor Sep 24 '19 at 14:42\renewcommand{\sectionmark}[1]{\def\rightmark{#1}}– koleygr Sep 24 '19 at 14:46\chapterpagestyle affects the\section? Yet, even when I remove\chapter, the problem persists. And the optional argument for thesectioncommand is not an option for me, because what is written there will make its way into the TOC, which is not what I want. – shevek Sep 24 '19 at 14:58fancyhdrdocumentation was way beyond my comprehension whatrightmarkis there for. – shevek Sep 24 '19 at 15:10\section[short text](long text}? – barbara beeton Sep 24 '19 at 17:38\markright. I see that's used in this answer in the (re)definition of\sectionmarkbut apparently isn't working. The next thing I'd try is using\rightmarkdirectly after\section. And if that works, I'd assume thatfancyhdrdelays its definitions until\AtBeginDocument; if true, then your redefinition of\sectionmarkcan be changed to use\AtBeginDocument. – barbara beeton Sep 24 '19 at 21:08markrightandrightmarkinfancyhdris: the redefinition ofsectionmarkIS working, see the comments to the answer of @koleygr. – shevek Sep 24 '19 at 21:36\rightmarkuses the content of what has been stored by specifying\markright. If\markright(or\markboth) hasn't been specified,\rightmarkwon't contain anything, so nothing will be printed.. (I hope this makes sense.) – barbara beeton Sep 24 '19 at 22:04