Low voltage switch to power a 110V pump, with a timer countdown (I think)

The previous owner of our house faked his way through improper hot water plumbing by running a recirculating pump 24/7 so hot water was always at hand. Wasteful of propane. I bought a smart product that keeps the pump off until it detects the movement of hot water out the water heater (e.g., when you turn on hot water). Then it lets the pump run for a couple minutes before shutting it off. Well, the electronic part of it failed. And the guy who runs the one-man company is a nightmare to deal with. So what can I do myself here? There's a valve that plumbs into the hot water line that completes the power circuit when water moves. That is mechanical and still working fine. How can I connect the two low voltage wires from it to....something.... that can connect up the power to the pump, and start a countdown of say 2 minutes until it disconnects the power again? Just typing this makes my head hurt.