Both rear signal lights flash.

Also, they stop flashing when the brake is pressed.

 

Evenin cord,
Your break light and the turn signal are the same filament. The other filament is your runnin lights. It sounds like you have a bad ground.

 

Cord, I agree with Hobbles. Try this. run a temporary ground wire from the battery negative terminal to the steel housing of the turn signal, just touch the ground to the housing while the turn signal is on. If that fixes it then you need to ground the housings.

My grandfather had this same problem on his 72 C20. I ran individual ground wires from the frame to each of the rear tail light housings and that fixed the problem.

Hope that helps

 

You can try new screws to fix the grounding problem or add a ground strap.