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That's perfect! Thank you! I had found something like that for \chaptermark but was never quite able to adapt it for the section.

I'm almost done with the fine tuning of my document, but there remains one unsolved mystery to me. I can break it down to this MWE

\documentclass[12pt]{report}

\usepackage{fancyhdr}

\pagestyle{fancy}
\fancyhf{}
\fancyhead[R]{\nouppercase {\rightmark}}
\fancyfoot[C]{\thepage}
\setlength ...