1991 Oldsmobile Cutlass Fuel pump power

Hi, I'm not sure which Cutlass you have, there are several? The initial prime comes through the fuel pump relay. Some systems have an oil pressure switch in the fuel pump circuit, just a redundant power supply to the pump, wired in parallel to the relay. Once you crank it enough to raise oil pressure, the switch closes and the pump will run, even without the relay. You may need to check circuits at the fuel pump relay, with extended crank.