What wire goes to the fuel gauge of a 1989 Cadillac fleetwood brougham?

There isn't a single wire dedicated solely to the fuel gauge in a 1989 Cadillac Fleetwood Brougham. The fuel gauge receives its signal indirectly through a combination of circuits and components. The signal originates from the fuel level sender located in the fuel tank. This sender has a variable resistance that changes with the fuel level. This resistance change is then interpreted by the instrument cluster's fuel gauge circuitry.

Therefore, you won't find a wire labeled "fuel gauge." You'll need a wiring diagram specific to your 1989 Cadillac Fleetwood Brougham to trace the circuit. The wire(s) you're looking for will be part of that circuit, likely originating near the fuel tank and terminating at the instrument cluster. The wiring diagram will show the correct wire color(s) and their connection points. You can find these diagrams online (sometimes for a fee) through sites specializing in automotive repair manuals or in a repair manual specific to your vehicle's year and model.