Enforce duty cycle?

Wondering if there is an easy/elegant way to accomplish what I’m looking for.

So, simplest explanation: when a given switch is on (and only when that switch is on), I want to toggle another switch off and on with a given duty cycle.

Slightly longer explanation: I have a hot water/radiant heating system. The system has 3 pumps. The pumps are currently triggered with temperature sensors and generic thermostat entities. I’ve noticed that the heating seems to work best when the system first turns on, and then it seems like it gets ‘tired’ after a while (maybe pump is over heating?). I’d like to turn off the pump for maybe 10 minutes for every hour its on to allow it to reset and see if it makes a difference.