The yellow wire on the ignition switch supplies power to the starter solenoid when you are twisting the key to crank the motor. The oil pressure switch is not the same as the oil pressure sender. The sender has 1 wire and is located on the top rear of the engine by the ignition coil. The oil pressure switch is located on the port side of the engine below the exhaust manifold at the rear just above the oil filter. If you have a remote oil filter it is just above where the lines to the oil filter come off the engine. There are 2 or 3 wires on the oil pressure switch. One goes to the fuel pump, one goes to the alternator, and if there are 3 wires, one goes to the starter solenoid. When the starter engages (you are cranking the engine) voltage from the starter flows through the oil pressure switch and to the fuel pump or directly to the fuel pump, supplying fuel to the engine. When oil pressure picks up or the starter is no longer engaged, the switch opens this circuit and closes the circuit from the alternator to the fuel pump. This allows the fuel pump to continue running after the engine is started. If the oil pressure switch is not working properly, one or more of the circuits may not be functioning.
It sounds like the starter circuit fuel pump is working, supplying fuel to start the engine when cranking but the alternator circuit is not. If you jumper the wire from the alternator to the fuel pump, the fuel pump will run whenever the key is on, regardless of oil pressure. This should allow your engine to continue to run without holding the key and would indicate the oil pressure switch is faulty