On the 82 Trans Am, the right blinker like comes on when I put the parking lights on. It's not fully bright, but slightly there. The blinker works fine, and it doesn't happen when the lights are off. Any ideas?

 

Check the wiring harness leading from your steering column to the flasher unit. Look for chafing where it contacts other wire bundles and insulate any damaged wires. Your squawk sounds like a short circuit between the parking lights and the turn signal.

 

By design, the front turn signals glow dimly with parking lights on (they use dual-filament bulbs). If only one side is lit with your parking lights, then the other one probably has a bad bulb.
But if you mean that the passenger side is brighter than the driver side front park lamp, I'd switch bulbs and see whether the problem switches sides. That would point to a bad bulb.

Since the F-body parking lamps are interconnected with turn signals, a bad bulb can wreak havoc on these two circuits.

Let us know what you find.
Lou