There is a small set screw, or maybe two, that make the red moving pointer attach to it's drive shaft.
The unit I used to use had the red pointer slip at some point in the past, so that it would point at like 59.5. Then sometimes there would be a dead bang when it timed out.
So there is some mechanical shut off issue around zero I had, that you have in some manner too.
I know this is not a solution, but I hope it feeds your problem solving process.
I sold mine after I discovered the joys of f/stop printing. I went to an electronic timer, because the trusty old time o lite did not have the precision I wanted.
The time o lite, with its auto reset of the preset printing time was a very nice step up from my old gralab 300 I started with though.