Is the switch on the tranny a part that goes bad? I have no reverse lights!
Just completed a restoration of my rear 1/3 of CJ and all the tail wires too...
Wires run the + 12 volts and get the ground via the body and the mtd screws/bots on the rear lamp housing.....
If your other lights work.... then you have the ground circuit for R Lamps (most likely)
1... There is a fuse for the Reverse Lamps..... it has its own fuse for my 1978 and most likley the same for your 1980s. Ck to see if fuse is blown or there. MINE was missing one and one of few faults...
2...
Transmission switch is normal open and closes when you put in reverse. This is switched power and ON 12V with the engine running only... If fuse cks out... then one side of switch should have 12+ and when in Rev the second side should be 12V+ also... If both sides show 12 V the Rev Switch is working... A wire with tan insulation and black trace will be running to and from the REv Switch..... I think that was the color on mine and most likely yours...
The power runs down the Drivers side of cab and down the drivers rear corner.... There are a few connectors in the back corner of the jeep and they get pretty beat up from the mud, water, and junk the rear tires kick up. My rev light wire was broken off. I replaced all the connectors and rewired the back end... gas tanks was down and axle was out... so it was the best time to do the work... The wires in the back corner are color coded and listed in the elect diagrahms in the Jeep FSM.
If you have to rewire the back quarter.... say so.... I will tell you what I did and it was a good solution and did not break the bank... was cheap used 3 trailer connectors pairs $2 each... so $6 in connectors, and $10 in high performance heat shrinnk and some extra wire..... This included wires for the trailer whip too....