I suspect this is a sedan - the sedans seem to have more problems in the rear lights than the wagons do. True?

If your son or a friend has a voltmeter or at least a 'test light' then he will have a much better chance of figuring this one out.

The bulb failure detector (bulb failure warning relay, BFWR) monitors brake lights, tail lights and low beam headlights. Ignores backup lights and fog lights, if you have them. Failure in the BFWR can disable any of the circuits it monitors. So you might need to replace the BFWR. Located under the dash, far left, in the lip of dash where the front face curves down and in. It's a red-orange can, about two inches diameter and 2-3 inches long. Has many connector pins, like maybe a dozen or more, so it's hard to pull it free of the connector.

Failure of ground connections is always a possibility. There's a ground screw near each of the rear light assemblies with a wire going to the screw.

Or the failure could be in the wire harness leading to the rear lights or in the connectors there between the harness and the bulbs. There are plenty places where the electrical continuity can be broken.

Wire harness leading to the rear lights arrives at left side light assembly. A white nylon connector clips the harness to the circuit "board". From there, additional wires carry appropriate current over to the right side lamp assembly.

Backup lights - our '90 is set up this way - I'd guess the '83 is likely same.
Note that the backup light power for BOTH sides arrives via the harness and goes to the connector and into the circuit board clip. From there another wire picks it up and carries it to the other side. So if you pull the connector at left side the right side backup light goes out. You need good contact at the left side connector for the right side backup light to work. Tail and brake lights have separate wires for each side.

If you pull off the connector, you can use thin test probes to test for voltge there. That is, circuit board and bulbs and bulb holders may or may not be OK but you can test to see if voltage is arriving there at the wires. This will help narrow down the problem.

Hope this helps.
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Sven: '89 245 NA, 951 ECU, open-front airbox, E-fan, 205/65-15's, IPD sways, E-Codes, amber front corner reflectors. Wifemobile '89 245 NA stock. 90 244 NA spare, runs.