How is the grounding for the turn signal. Sometimes lights, with insufficient grounds, do weird things like that. System has black switched power to turn signal relay that connects to the light gray
Light gray goes in to headlight bucket, connects to handlebar switch gray. Output of switch is now blue or orange, not much else going on
Try finding a "sweet spot" that you can get the one light to actually blink. Inside of the turn signal switch there is a slider that carbon tracks and assorted grossness build up on and stop the proper contacts from working. Spray QD cleaner or something up in the switch thru the little hole in the bottom of the switch. Now try to see if you get anything to work. If it blinks justtttt before it is all the way switched you have a dirty TS switch