Park lamps iluminate with brakes

Hey Guys, I'm wondering if anyone could help point me in the right direction with an electrical problem I'm having. I've found similar issues guys have had with the search function, but they seem to be related to the hazard flasher circuit.

This is a 1964 Valiant - no hazards. When I activate the brake lights, my park lamps come on. I'm working by myself so at this point I'm not sure if its the turn signal filament or if they're actually the park lamps. I am not aware of any other lighting issues other than no license plate lamp.

Things I've tried so far:

• I've replaced the turn signal switch and harness. This was suggested in a few forum posts as well as at a local Mopar restoration parts dealer. They sold me a new unit and the problem has persisted.
  
• Brake light switch replaced.
• Headlight switch pulled, contacts cleaned and connector inspected.
• Not that I thought it was related, but the turn signal flasher was replaced.

Any suggestions? Thank you!