Have you checked all the fuses? You could also measure the voltage at each fuse (relative to the car ground), and there should be 12volts on each fuse with the ignition switch on (and some will be on even when the switch is off).

Also, I believe the two wires that deliver power to the rear lights you're having trouble with are a yellow-red wire and a yellow-black wire. There is a connector for these (not sure where it is in the 1981 model), and so there might be an issue with the connector. It's likely above the rear wheel arch on the driver's side.

Also check the ground connections for the light assemblies in the trunk. These ground connections are notorious for going bad.

-Bryan

Do you have a wiring diagram? If not go to the mirafiore.com website and download one from the library. Membership is required but free. As Bryan said the grounds in the trunk are problematic, as are all the grounds on these cars after 40 years but usually fine after a cleanup with sandpaper or a wire brush in a dremel. To me the wiring is not intuitive the way the circuits are split. Front right/ rear left on one and vise versa on the other. Logical yes but ......... Also if you don't have an owners manual get one of those also and there is a page that lays out what functions are on which circuits and what value fuse is supposed to be on that circuit. Hope that helps.