Check the wiring at the sending unit in the differential. Mine had corroded through, and stopped working.
Bet you a donut that it's the wiring back there.
You can pick up replacement wiring from the stealer or BMA; pop the plastic cover on the connector body, remove the original, and put the new connectors in. Of course, the wires will both be green now, since the replacement wiring does not come with the proper color-coded wires, but it's not hard to do.
If my records are right, the part is Cable Socket (pigtail) 61 13 0 007 445.