This seems to sound odd for some people but I think this idea is not that bad.
A normal clock and maybe even a stopwatch.
I remember many gigs were it was very important to leave the stage in time.
So it was with many contests in earlier years and also when playing slots on big stages with tough shedule.
Of course, if you know ur setlist well, you know how long it takes, but soundcheck always varies and sometimes u may have a break or problem during the set that throws you out of the timetable.
Also, I know the situation when a tech or moderator stands beside the stage and wants to say u should play your last song but u got still 3 or more songs on setlist.
In this situation it is always good to know if u are realy out of time or the tech is wrong.
Also good for soundcheck to know how much time left till you should start ur show.
I don't wear a watch and I think the only thing worse than having ur phone in ur pocket during gig is taking it out on stage to check time.