My brother's GSX's fuel gauge always reads full, regardless of the amount of gas in the tank. All fuses are good, no known wiring issues. Is the problem likely the fuel sending unit or perhaps the gauge itself? Assuming it its the sending unit, where is the best place to purchase one?
I have been working on aircraft instrument systems since the 1980s and the fuel quantity indicating system in a Wichita-built bugsmasher of a certain age is basically the same as what you’d find in a car of that vintage (e.g. Cessna used Stewart-Warner and Rochester gauges for its piston single aeroplanes for quite a while). A car fuel quantity sender is just a variable resistor usually actuated by a float moving an arm that is attached to the resistor wiper. When the resistor (sender) is at zero ohms, the gauge reads empty. When the gauge reads full, the resistor will be at some non-zero resistance, but likely to be less than fifty ohms. I suspect that your brother’s gauge is pegged past full, which is a symptom of an open circuit or a high resistance. It could be a bad earth as already described, it could be a bad sender, or a bad connection between the gauge and the sender. It’s unlikely to be the gauge, but you can check it by disconnecting the wire to the sender and earthing it out on the body of the car somewhere. If the gauge reads empty, it’s fine. The fuel gauge on the ‘71 GS Stage 1 I recently bought is reading past full and there is a wire dangling between the fuel tank and the differential; I suspect that this is the reason it doesn’t work but I have yet to confirm it.
GM sending units operate between 0 and 90 ohms. I have been finding the fuel is corroding the internals of the sending unit. This creates high resistance causing the gauge to read high. Jason did a great write upon testing and operation of the fuel gauge. https://www.v8buick.com/index.php?threads/fuel-gauge-and-sender-operation-and-diagnosis.330220/