Press the Brake the Parking Lights come on.

Your parking lights should have their own circuit off of the headlight switch going directly to the parking/tail lamp filaments , Black wire originally according to a 73 Dart wiring diagram I looked at.
The black wire gets power from headlight switch and runs directly to the rear it remains Black and front parking switches to a black/yellow wire .
If your getting power from the brake switch something is wired up wrong or its getting a back feed somehow.
I would double check your wiring, if it worked fine before it was re-wired.

http://www.mymopar.com/downloads/1973/73DartB.jpg

http://www.mymopar.com/downloads/1973/73DartA.jpg