Do you have a gauge that follows the pressure, or was it pegged when on, and not when off? If so you may have a sender that only registers when the pressure is on, and off, not the variations in pressure. The sender in this case could be the issue. They do go bad, and you have to replace it with the proper one.
I do not know if the oil pressure switch will kill the pump. According to the Haynes manual, the oil pressure switch bypasses the fuel pump relay to allow the engine to start when there is proper oil pressure. From what I understand, as long as there is a spark signal, the fuel pump continues to run.