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On my 1977, the pair of inner tailights & backup lights do not work. The brake lights, directionals, and running lights on the pair of outer rear lights work OK. Any ideas? The bulbs and sockets are OK. I realize it may be 2 different problems, the back up lights and inner lights, but don't want to invest in a new back up light switch if the problem is something else. I assume that the inner lights also serve as running lights, but have never seen them work in the 3 months I have had the car.
If nothing on them works, I would trace the line and check grounds.
You should also take a meter and test for 12v to the sockets, if you have voltage, it almost has to be a ground.
The inner lights are just reverse lights and reflectors. There are no other lights there. They have a single filament bulb only.
Assuming a good ground, which you seem to have since everything else works, the problem is probably the reverse light switch. Find the switch (on transmission for manual, on shifter fro auto) and try bypassing it. That will help you diagnosis.