Here is a best guess without seeing the wiring diagram. The challenge is that when the engine is first started the
oil pressure is assumed to be "0"psi. You need a way to get the pump running while cranking the engine. The connection to the starter should go to the solenoid side of the starter. This provides + 12v to the pump positive terminal during cranking. This effectively bypasses the safety cutoff switch during starting. Once the starter solenoid is released and the starter disengages from the flywheel the
oil pressure safety switch is back in the circuit. Assuming now you have adequate
oil pressure the switch will supply power to the pump and maintain pressure in the fuel system. One additional safety feature I used in my wiring is to use a fuel pump relay to cut down on the heavy guage wiring required and wired the circuit described above into the control side of the relay. Lastly the factory Mustang used a roll over switch that has a NC(normally closed) set of contacts when the car is upright. If you should ever roll the car the switch opens and the fuel pump is automatically cutoff reducing the chance of a fuel spill and fire.