Darn Parking Lights!

It might be as simple as grounds. Stab a meter into the metal of the socket shell and the other probe to a known ground like the engine block. If you are in the rear, something like the trunk latch bolts are a good ground, just get to "bare" metal. With the lamps energized, exhibiting the problem, you should read NO voltage between the lamp shell and body ground

Otherwise, might be something crossed/ crimped (pinched) /. melted in the harness. If you can disable/ isolate the circuits by pulling fuses, then inject power back in at some point that might at least tell you that very thing is happening.

The only common thing really, between park/ tail and stop/ turn is the bulbs themselves