Hello Thorsten,
To change the timer display to a red line at the top of the page, just style a div element as follows in the file "..\mod\quiz\templates\timer.mustache":
<div id="quiz-timer" class="quiz-timer-inner py-1 px-2 ml-auto" role="timer" aria-atomic="true" aria-relevant="text" style="background-color:#F00;color:#FFF;width:100%;text-align:center;">
It is certainly the fastest way, but not necessarily the most convenient. First of all, you need to have access to the Moodle files, which you don't have if you are not the site administrator. Second, the change will be overwritten with the next update to Moodle.
Regarding the little script I had suggested to Mawuli, I found the problem when looking at the code on his installation. I don't remember but it was a small bug, maybe related to the language used for the name of the selectors or something else.
What do you see if you inspect the timer? (In Chrome, place the cursor on the timer, click the right mouse button and select "Inspect".)