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This is going to be a faulty Fuel Level Sender. This is actually a known problem by Ford, and they have issued a Technical Service Buleetin on the issue:
ERRATIC FUEL GAUGE
ISSUESome 2005-2006 Mustang vehicles may have an erratic fuel gauge concern (does not read Full or reads Empty when tank is full). This may be caused by poor electrical connections at the fuel sender, at the in line harness connector, and/or faulty fuel sender card.