1981 242. Back-up bulbs are good, sockets are clean, but no back-up lights. I'm guessing the switch on the driver's side of the tranny is the culprit. I can test it for continuity in reverse and out of reverse. If it fails, what's the easiest method to remove and replace the switch? It's a tight fit. The transmission is an M46.
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Thanks to everyone for the help, Doug C. 81 242 Brick Off Blocks, stock; 86 240, 129K, once in Rolling, now smashed quarter panel thanks to driver of an F150. Daughter safe in her Volvo.

Thanks. Advice worked. I took both light assemblies out, cleaned all the contacts in all the sockets, and on the circuit boards, cleaned all grounds and cleaned the plug in connectors. Basically I cleaned every contact I could find. When I put it back together everything worked. The lights are brighter now because I cleaned all the dust out of the lens assemblies, and maybe from the cleaner contacts.
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Thanks to everyone for the help, Doug C. 81 242 Brick Off Blocks, stock; 86 240, 129K, once in Rolling, now smashed quarter panel thanks to driver of an F150. Daughter safe in her Volvo.

Mine was the switch in the shifter, moved it slightly forward...1mm and it fixed.
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Chuck B '89 245 DL, '85 244 DL

I went through this with my 1991 automatic. took apart the gear selector lever to get to the switch, cleaned and tweaked it, twice. Looked high and low for a fuse.. checked and rechecked everything. As it turned out it was a poor contact at the right side tail light plug, where the wire harness plugs into the tail light and printed circut. This plug supplies ground two both backup lights. This is a common trouble point, I guess because water can leak down on the connection. Mine was all funky and corroded. good luck.

I'll second this, had exactly the same problem with my daughter's '84. I cleaned the connection on the printed circuit on the left side and the lights worked again. You can measure for the presence of voltage and ground at the printed circuit.