Have you tested that the sender unit isn't faulty ? If it's shorting internally somewhere the light will come on regardless of the oil pressure. I don't have the wiring diagram to hand but typically the 12v supply goes to the warning lamp first, then to the sender switch, and then to earth. If the wire between the lamp and the sender is shorting out somewhere, that too will result in the lamp coming on.
For the first fault, you need to try a known good sender to see if the fault is still there. For the second, disconnect the lamp-sender wire from the sender. If the light stays on then the fault will be in that wire.
