Parking Brake Light Problem

Weird cross connects and poor grounds can really screw you up. I would yank out all the LED equipment in the turn/ stop circuits and reinstall bulbs and conventional flasher ONLY to confirm that the system works properly. You may have screwed up wiring the TS switch as example, or it could even be defective / mis wired. Get that working, and then reinstall the LED stuff and go from there.

CHECK SOCKET GROUNDS or even consider soldering ground pigtails to the socket shells and bolting to a good ground point on the body.