If the two fillament bulb (Stop and Running) are reversed then the Stop bright light would be ON with the light switch pulled out one click to Running/Parking light position. If you then applied the brakes it would show no change as the bright light would overpower the dim fillament.
Mike B

That thought occurred to me also. If the rest of the wiring checks out, maybe try reversing the two wires that go to that two filament bulb. The tail lights should be running the dim filament of that bulb and the brake lights should be on the bright filament.