the gas gauge on my 04 mustang reads empty, today it has circled past F to E

Hello, you have a concern with the wiring to or from the fuel sending unit, or a problem with the sending unit itself. Testing is quite helpful using a diagnostic tool where you can actually actively command the gauge with various fuel levels to make sure the gauge is responding properly using the instrument cluster module and wiring. The diagnostic tool will also show where the sending unit is positioned, relative to the fuel in the tank, and give you a sense of the fuel level that is being measured -- accurately or not. Once you perform testing, you can see what will need attention.