Opinions/Improvements on a run periodically/timer function in Python 2.7
I don't think you do need the scheduler for that, at least not for how you use it.
Your loop schedules 1 event and just afterwards waits until it's finished, since run() waits until the scheduled event(s) are completed.

You can achieve the same by just sleeping for runtime seconds and calling runme() afterwards (you have to sleep before, since the scheduler delays the action for runtime seconds).

Also note that random.randrange(intsmall, intlarge) will return a value between intsmall and intlarge - 1, so your random time will be between 40 seconds and 99 seconds.