Q&A

 Master

Most likely it's the fuel gauge sender in the tank in a module on the right side of the tank, separate from the fuel pump which is on the other side. It's accessable under the rear seat, through an access hole in the floorrpan. the fuel lovel sender will have electrical connections but no fuel lines. If you see fuel lines, that's the pump, not the sender.
There's more: the sender wiring goes to a "Smart Junction Box" in the passenger's kick panel area. Reportedly, water can leak into the SJB and cause problems. Check this out. the fuel sender connector is black. Also check for wiring damage under the car from wiring touching the exhaust.

This is pretty common on the 2005 Mustangs, it's caused by failing stepper motors in the instrument cluster, they control the movement of the gauges. There's a guide on how to fix them here - www.2005-mustang-speedometer-problem.com