Q: Fuel gauge is erratic and inaccurate

Hello. Based on the symptoms you are reporting, your supposition is correct. The sending unit is typically a variable resistance element (i.e., a potentiometer) that can be tested by the Mechanic with an ohmmeter. These units can physically bind. The contacts can get worn and even fuel deposits or varnish can degrade the contacts, altering the intended resistance. It is also possible to have wiring faults in the sending unit circuit that will mimic a failed sending unit, for example you could have a short to ground or a high resistance connection but typically the sending unit itself is bad. If the unit does test bad, on removal the Mechanic will still typically check to be sure the movable arm of the unit is not simply physically hung up or restricted by, say, an out of position vapor line in the tank or misplaced wiring, again not typical, but things that will need to be checked to be sure you do not replace a perfectly good part. At your request, a certified technician from YourMechanic would be pleased to give you a definitive diagnosis of this possible electrical problem and a cost to repair.