I have a whole-house fan and as the days get colder I find that it's a bit too strong even on the "low" setting. So, I would like to add a timer-like device to the circuit that would do something like a duty cycle: "5 minutes on, 10 minutes off, 5 minutes on, 10 minutes off" preferably with the ability to adjust the proportion of on time vs off time; however all the "timer" in-wall devices I can find are like... programmable per-day kind of devices instead of interval-based.

Does anyone know what the magic search term is for duty-cycle/interval-based timer devices? Or if they even exist in the first place...