Some pumps have their own relief valves.Really, I offer a tried and proven and very widely used scheme in post #18. Evidently nobody understands how it actually works. ALL of the other schemes depend on electrical power and quite a bit of circuitry and hardware.
Certainly a low pressure relief valve is a totally non-electronic method, and possibly it will be a challenge to come up with the right one. BUT it is vastly simpler and a lot more reliable.
Why the pump needs to stay on when tap is off is a question. Why does pump keep running when flow is not needed? In hydraulics the pump is usually connected directly to mechanical drive engine, always on. Maybe it's better to control an SSR for the pump, and, have a mechanical relief loop for when the tap goes off but pump is still spinning for short period. Blow-off valves for turbo setups work this way, to relieve surge.
Even simpler is two different hose sizes. Example, run the main line as 3/4, then just T off the pump 3/4-3/4-1/4, and just run sturdy 1/4 back to the tank. Yep, the loop always flows, but 3/4 will drop the psi a lot more when tap is open, so it takes most of the flow. Close the tap and the psi in 1/4 goes up, but it still allows loop flow to keep pump from stalling or cavitation. I gave example, but sized right you don't need electronics or valves.
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