Rear Rear Axle temp inop..ideas?

Possibly a broke wire around the tandem from movement over the years.

 

Center wire??? Your KW has a 3 wire sending unit? Never seen a 3 wire, for a diff sensor. Like I said if its a single wire ground it out to a clean spot and see if the gauge moves, if the gauge moves its the sensor. On a 2 wire setup connect them together and see if the gauge moves. If the gauge doesn't move on a 2 wire then it could be a gauge or a wire, Ohm the wiring at the back of the gauge to check for continuity

 

If all else fails, make sure and ohm the wire from the sending unit to the gauge. I had a fan come apart and get the wiring for the lights, dint have any markers so we hunted and hunted, couldnt find anything, the wire for the markers had 12v, got p.o'ed and went to yank out the harness, the wire was all but broken except for one strand. That let volts through but no amps. Just my 2 cents.