Bad Ground(s) for sure.

Check them all both at the turn signals and most definitely at the cluster. The symptom of your fuel gauge, and also likely temp gauge pegging like that with the lights on is a sure sign of a bad ground. Your cluster is finding ground through the senders and/or turn indicators.

Bet you've either got a broken pin on the circuit board or just simply a poor or corroded ground somewhere. It never hurts to add a secondary ground wire simply because you can't trust 50 year old wiring.