Turn signals light on when the brake pedal is pressed- 1969 Dodge Dart

Instead of throwing parts at it, try to figure out what is going on.
This and the link to the Chrysler tech booklet explains how the turn signals work in general.
Turn signal fun
1967 Chrysler Imperial Electrical Accessory Circuit From the Master Technicians Service Conference Session 236 (this link works and explains the turn signals and hazzards)

Then look at your car and the wiring diagram to sketch out how the stuff actually connects in your car.
It might be just as shown in the examples, or some slight changes in how connections were made. pretty sure yours has the combined turn/brake/tail bulbs with two filiments.

Take each bulb out and look it. It could be something as minor as bulb noit properly seated or two wires touching that shouldn't.

Brake light switch gets power from one of the always hot fuses.
Hazzard lights. Same.
Turn signals get power at the fuse box from a fuse that's only connected when key is in Run or accessory positions.