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The quick way to tell: with the key on and the car jacked up, disconnect the sending unit at the tank. If everything forward is OK, the dash guage will go to one extreme or the other (empty or full). Then jumper the connection to a good ground (sometimes hard to find on our cars). It should go to the other extreme. If so, you have a defective tank sending unit. If not, the problem lies forward, usually in the guage itself.
"Way past full" means an open circuit. Check the connections at the sending unit, see if there it +12v back there on the tan wire (going from memory here). Also check the ground. If you don't have +12v back there, the problem is either in the wiring, the connection at the gauge, or in the gauge itself.
id say the connector is off
its semi reachable if you pull the rubber boot off from around the gas cap, i think its on the right(passanger) side and you shoudl be able to reach the eletrical connecters. Beware, there shoudl be a hose connected to the rubber boot that hangs down the back to drain water out of it, just remember that its there and generally loosly held on.
Id say that if somethign broke, its the sender, but they tend to die gradually, thats why i ut my money on a loose connector
Dont forget, it coudl also be the connection to the back of the gauge too.
I had this happen on two different instances. One, on my '68 I had dim tailights and gauge way past full. On that instance, it was where the black wire grounds on the frame near the antenna base/left rear tailight assembly. Redid the "ground eyelet" and this fixed the problem. 2nd instance was my '74. Gauge was way past full and it was where the tan wire literally came out of the "bundle connection" on top of the steering column. I pulled the "bundle connector" apart, re-inserted(snapped in), the tan wire "pin", snapped the "bundle wire" connector back together and my '74 was fixed. Both instances in my case it was a repair, not a sending unit OR gauge. :D
I massaged the ground and sender wires and one or the other was not making good contact.
Life is good here in CenTex: daylight savings time, wildflowers, sunny and 83 and now an operating gas gauge!