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.
I'd start at the brake light switch with my icepick tester. Confirm there is 12v+ and then depress the pedal to confirm there is 12v+ on the other terminal (switch leg side). If that checks OK, then follow the switch leg wire off of the switch and see where it goes. It should go to the rear Stop lights, but may pass through the dash wiring first (which is where I suspect you have your issues).
Since you have two light bulbs at the rear your brake light circuit does not need to pass through the turn signal switch. Your trun signal should be a simple 3-wire switch with a 12v+ hot wire going through the Flasher and then going up the collum and the Left and Right switch legs coming down...
Mike B
