Gas gauge always full (1968 Barracuda)

Is the fuel gauge wire plug in on both ends
Not sure what your asking. Fuel gage wire plugs in at sender. Fuel gage has 3 studs on it that go to circuit board. One stud is 12v in to the internal IVR, second stud is the 5.5V output that feeds oil psi gage and water temp gage, 3rd stud is for output to fuel sending unit.

Quick way to check these 3 gages with power off is jumping a 9v battery across their terminals one direction they will rise and peg, other direction they wil go to the low side. This lets you know the gage part of the equation is working.

All this plugs into the "gatlin gun" or cannon plug connector. Ine wire from there gives the 12v feed to the circuit board to gag gage, and 3 of those pins on the circuit board go to wires that go to the sending units.

The gages not working is pretty simple to figure out, also make sure the cluster is grounding well to the dash frame this can also be a source of problems. Some guys will run an extra ground wire from the gage housing to a dedicated screw on the dash frame to make sure it is grounding.