There is no any sensor providing info to engine ECU regarding fuel presure. On ignition engine ECU will fire fuel pump a fraction of time to build up a pressure in the fuel system to be ready when you turn starter on. Engine ECU will fire fuel pump to build presure by default.
Fuel pump is lubricated by fuel, so you should not let fuel pump to starve from fuel in the tank.

It is alittle bit odd that you do not have 12V with multirelay attached. Have you checked that you have clean contacts on the relay and multiplug?

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