If I recall (and that's no guarantee) the ECM provides power once the engine gets over 400 rpm
The prime signal only lasts a few seconds after key on.
If after the pump stops priming, you turn the key to crank the engine, oil pressure starts to build, and once past a point that relay provides fuel pump power during cranking, when the engine fires and gets over 400 rpm the ECM then provided constant fuel pump power.
You can test if the fuel pump is working at all, by providing a temporary source of 12v to the fuel pump prime connector. The black one wire connector hanging loose a few inches behind the alternator. The underhood light source connector is a good source of 12v to jumper over to the prime connector. Try that and see if the pump runs. If it does the wiring to the pump and the pump its self are good. Otherwise.....