\documentclass[twoside,openany]{book}
\usepackage{lipsum}
\usepackage[pagestyles]{titlesec}

\renewpagestyle{plain}{
    \sethead[\firsttitlemarks\bfseries\ifnum\value{section}=0 \thechapter\else\thesection\fi][][]% even-left | even-center | even-right
    {}{}{\bottitlemarks\bfseries\ifnum\value{section}=0 \thechapter\else\thesection\fi}% odd-left | odd-center | odd-right
    \setfoot[\thepage][][]% even-left | even-center | even-right
    {}{}{\thepage}% odd-left | odd-center | odd-right
    \setheadrule{0.4pt}
}
\pagestyle{plain}

\begin{document}

    \tableofcontents

    \chapter{Header Test}
    \section{Sec1}
    \lipsum[1]
    \section{Sec2}
    \lipsum[3-4]
    \section{Sec3}
    \lipsum[5]
    \section{Sec4}
    \lipsum[7]
    \chapter{New Chapter}
    \section{Sec5}
    \lipsum[2]
    \section{Sec6}
    \lipsum[6]
    \section{Sec7}
    \lipsum[8-9]
    \section{Sec8}
    \lipsum[10]
    \chapter{GAH}
    \lipsum[1-4]
        \chapter{New Chapter AAAA}
        \section{Sec5}
        \lipsum[2]
        \section{Sec6}
        \lipsum[6]
        \section{Sec7}
        \lipsum[8-9]
        \section{Sec8}
        \lipsum[10]
        \chapter{GAH1}
            \section{Sec8}
            \lipsum[10]
            \lipsum[1-4]
                \lipsum[1-4]
                    \lipsum[1-4]
                        \lipsum[1-4]
            \chapter{New CHAPTER AAAAA}
            \section{Sec5}
            \lipsum[2]
            \section{Sec6}
            \lipsum[6]
            \section{Sec7}
            \lipsum[8-9]
            \section{Sec8}
            \lipsum[10]
\end{document}