Here is a Ford Service Bulletin related to the issue:
19098 MULTIPLE VEHICLES - SULFUR BUILD-UP ON FUEL LEVEL SENSOR - ADD "CHEVRON TECHRON PLUS FUEL SYSTEM CLEANER" TO FUEL AND FILL WITH FRESH FUEL GASOLINE OR DIESEL VEHICLES MAY EXHIBIT ERRATIC FUEL GAUGE READINGS, ILLUMINATED MIL, AND DTC P0463, P2068 AND/OR B1202, B2627 MAY BE PRESENT. THIS CONDITION MAY OCCUR DUE TO SULFUR CONTAMINATION FOUND IN SOME LOCAL FUELS WHICH MAY CAUSE TEMPORARY CONTAMINATION OF THE FUEL SENDER CARD. BEFORE REPLACING ANY COMPONENT, CLEAR DTC'S, DRAIN FUEL TANK (IF FACILITIES PERMIT), ADD TECHRON CONCENTRATE PLUS FUEL SYSTEM CLEANER AND ADVISE CUSTOMER TO USE AN ALTERNATE BRAND OF FUEL. THE CONDITION SHOULD CORRECT ITSELF IN A FEW MILES. ADVISE CUSTOMERS TO UTILIZE THE TRIP ODOMETER TO MONITOR FUEL CONSUMPTION. REPLACEMENT OF COMPONENTS OR PCM REPROGRAMMING MAY NOT FIX THE CONCERN. IF CONCERN PERSISTS PERFORM NORMAL DIAGNOSIS AND REPAIR. OBTAIN THE NEW TECHRON PLUS FUEL ADDITIVE LOCALLY FROM YOUR LOCAL AUTOMOTIVE CHEMICAL SUPPLY SOURCE OR AUTO PARTS STORE.
EFFECTIVE DATE: 02/22/2006
My truck used to do the same thing as you describe. I switched fuel stations and added the Chevron stuff and my fuel gauge issues went away. I did a little research and checked the back of the chevron bottle and it did say "Can be used with diesel fuel in light-duty direct and indirect injected diesel engines".