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!

Find the harness connector under the right kick panel and disconnect it.
Then try your brakes.
If the front part lights come on with that disconnected the problem is not in the rear of the car, but forward of that connector.

If the brake lights don't make the park lights come on with that harness plug loose then the problem is in the wires, sockets or grounding of the brake lights.

In fact it is very likely a ground issue at the rear bulb housings.

Take the lenses off and get a ground wire connected to the body of the car.
Put something on your brake pedal to make the brakes stay on with the parking lights lit.
Then touch your ground wire to the base of each bulb.
The one that makes the park lights go off is the culprit.

The way I explain it makes it a one man job, but if you have a helper capable of pushing the brakes for you is all the better.