This is frustrating. I dropped the tank and pulled the sender, and it looks quite new (definitely not 43 years old!). I connected a multimeter and the sender is putting out 0 ohms and 90 ohms when it should. I hooked everything back up with a new ground wire and reinstalled the tank.
Then I put about 8 gallons of gas in, and the gauge is still below 1/4 full

I think I may have a miscalibrated, or broken, gas gauge. I'll see if I can find another one to test with.
The other thing I can do is find a variable resistor and see what resistance I need to apply to get the gauge to go to totally full. My guess is that it's going to be more than 90 ohms. :let_it_all_out:
One other thing I noticed is the gas gauge stays in the same position even when I turn off the ignition.