Fuel gauge

Yes, my oil and temp gauge work fine, it’s just the fuel gauge.
As far as testing continuity, I think it’s the purple wire do I pull that bulkhead off on the back of the gauge? I don’t wanna break it. The wiring back there is pretty good shape actually.
If you're referring to the large round plug on the circuit board, yes, I'd pull that to do a continuity or resistance test. Just spray it good with penetrating oil first and gently pull it straight out....don't pull sideways to get it loose or you might loosen the circuit board pins. If you're careful where you pry, using two flat blade screw drivers (one on each side), works well. Just be careful you don't cut a copper trace on the board.