1982 Oldsmobile Cutlass tail lights

Could use some information or details. Do the front running lights work? What about the dash lights? Do the brake and signal lights work? Why didn't you list the engine size and mileage? Engine size is needed to find the right wiring diagram. Mileage can suggest which common things to suspect. Have you tested anything yet? If so, what were the results?

Well, there's four Cutlass models and five engine sizes, so I just picked at random. The diagram shows a brown wire for the tail lights, but if you don't have dash lights, you shouldn't have front running lights either. The diagram doesn't show the light switch, so we will have to start at that brown wire. You'll have to remove the switch to gain access to the wires. Measure the voltage on that brown wire when the switch is turned on. You should have 12 volts. If it is missing, ...

By the way, have you checked for a blown fuse? That is the first thing to do.