Automated secondary fuel pump.

This product monitors fuel pressure and automatically switches on the aux pump when pressure drops:

https://www.flyefii.com/products/bus-manager/

Why add all this complexity ? Just have the electric pump on all the time no switch.

then confirm psi when engine off and electric pump on and psi of combination which will be a couple of psi higher when engine starts.

I agree with Julian above.  For example, the standard Van's RV-12 with Rotax 912 ULS is equipped with a full-time / always ON auxiliary electric fuel pump.  This supplements the standard full-time Rotax engine-driven fuel pump.  The thinking here is that a full-time aux pump means one less switch to remember, constant circulation of fuel to reduce the potential for vapor lock, and instant aux fuel flow should the engine-driven pump fail at an inopportune time.  If you so desire you can check the operation of the two pumps during your pre-takeoff check and inflight by observing fuel pressure values as you turn OFF and then turn ON the aux pump.  The standard RV-12 does not have a separate switch to control the aux pump -- the pilot uses the aux pump circuit breaker to deactivate the pump if so desired.  Some RV-12 builders have chosen to add a separate switch to control the aux pump.

This is one of the reasons that you should practice engine out emergencies on a regular basis.

Adding in a pressure operated switch is not as easy as you might think.

Think it through in detail...

Fuel pressure drops below 2psi switch closes pumps energizes, pressure restores.

And then the trouble starts.

Pressure restores, the pump shuts OFF, pressure drops, the pump goes ON, Pressure restores, the pump goes OFF.  Lather, Rinse, Repeat!!!

You will need to separate the Aux Flow from the Main flow and measure only the Main pump's pressure.

This will require re-plumbing the pumps in parallel instead of in series and installing check valves to prevent backflow/Back-Pressure across the two pumps.

Now it is getting messy with more items added that have their own failure mechanisms.  Keep It Simple!!!  KISS!!!

In reality, a fuel pump failure is a very rare event.

Fuel vapor events are way more common so the ON-OFF-ON-OFF cycle would not be out of line.

A typical Engine failure checklist runs something like...

Trim for Vy
Identify Suitable Landing Zone.
Turn Towards Landing Zone.
Fuel Valve/Selector ON
Ignition BOTH
Fuel Pump ON
Attempt RESTART

That is a lot of effort to eliminate ONE line  Item.

Now consider the Engine Failure (In The Air or at Impact) that includes a Fire.

How do you prevent the Fuel pump from Activating and feeding the Fire???  KISS!!!

The AUX fuel pump should be wired to STOP pumping when the engine Stops unless Intentionally energized.

I've simplified too much the system in my explanation, there must be some hysteresis to switch off the pump at (for example 5 psi) and swicth it on again for example at 3 psi.

I like too much 912 fuel system because it have a pressure regulator and a return line, so, you can feed the system in series with two pumps (mecanical and electrical) always, and the pressure remains at the correct level to not over flow the float valve of the carburetor.

But it is not the case of the 582 engine (my case), in this case I only have a mikuni pump, and the series electrical pum, so if I've got some air bubble in the mikuni pump there could be any problem. And if I get two pumps on I get over pressure on the carburetor float valve.

That the reason of my design suggestion.

I appreciate you opinion.

Thank's!