All the lights except for back up and headlights come together/ split off from the turn signal switch. Id start there if you're SURE the grounds are good
The park/ tail/ cluster illumination has nothing to do with the TS switch or the TS switch harness connector
Only thing near the TS switch are the brake/ TS lights. Of course they share the same harness down and past the left kick panel connector and on to the rear of the vehicle