Sounds like the "brake/turn" and "running light" wires were reversed somewhere in the harness. Or bulbs installed backwards which should be difficult to do without damaging something. Easy fix right at the socket if that's the case.

Definitely check the circuits with a test light. Looks like all the rear running light circuit wiring is black. They originate as a single wire running to the rear of the car before branching off to the individual lamps. Right turn/brake light is brown. Left turn/brake is dark green. If it was crossed up further forward, all the running lights on the rear should also be not right. All this stuff runs through an 8 pin connector behind the left kick panel.

3 wires run it all. Both sides doing the same thing? Front turns OK? Tag light OK?

The black wire on the horn relay runs through the bulkhead to the turn signal switch connector and should go to ground when the horn is pushed. That can be checked with a test light. It should also blow the horns when a ground source is touched to that pin on the relay. Constant 12v needed on the other pin.