Is it common to default to a signed integer for tracking a timer? I realize being unsigned it would still overflow but at least you'd get twice the time, no?

Some C programmers take the view that unsigneds have too many disadvantages: undefined behaviour for overflows, and weird type promotion rules. So, they try and avoid uints.

If you get to right before you need to be (taking as long as you want), then wait until overflow, then you still have 12h to do the last tiny part if it's unsigned.