Sound like you have an open circuit. Check the resistance at the trunk where the rear harness plugs into the fuel sender extension.
I was at the store, shut off the car, went in and shopped, then returned to the car, started it and my fuel gauge went to max+. I grounded the wiring harness at the trunk and made the gauge go to empty...so I knew the rear harness and gauge was okay. I checked the resistance from the fuel sending harness and got 0 ohms. I had to change the fuel sender. I got the aftermarket from Rick's First Gen and had to send it back 2 times. Below a 1/4 of a tank the fuel gauge would stay at empty! I had Rick's send me a AC Delco, and I've had no problems since.
68 "Pro-Touring" Ragtop SS