TX Farmer is right. We had one several years ago that did the same thing. Wiring harness that reads oil pressure, header up and down, and I think one more function,but I can't remember what it did. Replace it and you will have your problem solved. Like he said it was a mice issue in our case.
Ground the 705 wire at the sender to see if the light goes out. If the light goes out then the sender is bad or no oil pressure. Wire 705 is the sender and 10 is the ground. This goes to connector 701 engine harrnes and to connector 402 which is the cab harness on the right side of cab to connector 509 is the warning display panel. If you ground the 705 wire at any of the places the light will go out. If not then the display is bad. If the light goes out at one and not the next then the wire is broke.
i would almost bet it is a ground problem where it will pass high amperage but not low, kind of like a situation where a digital volt/ohm meter will show power but an old fashioned test light won't light up. if you have not done so i would clean all the grounds i could starting with the easiest ones on the battery first. i also would get a good cat in case it is mice damage so it does not get you again! like the visa commercial says...... "cat food 14.99, a barn cat chewing on a mouse priceless".