I think you would smell/see a fuel leak of that magnitude.
In years past, I owned a Chevy pickup (i've already done lots of therapy for that offense) with a manual tank switch. The second tank was installed by the previous owner and didn't include all of the factory piping/tubing. If the main tank was full and I was running on the secondary tank the excess fuel that the pump provides to the engine would route back to the main tank. When it got overfull it would just spew out the side of the truck.
Again, if you're losing a lot of fuel you should see it or evidence of the spill.
Do you have a locking fuel cap? Could someone be stealing the fuel from your truck?
2001 F350, CC, Lariat, 4x4, SRW, 7.3 PSD, long bed, 6 speed, K & N intake and filter, air bags, Powerslot rotors, Hawk LTS pads, Energy Suspension front sway bar bushings, foil delete, Moog ball joints, HPX, FRX, RiffRaff boots and plenum inserts, AIH delete, factory rear sway bar, Marinco plug. 110K
Oh, and the valve handle is inside the cab, while the actual valve will be on the underside of the cabs sheetmetal in plain sight, where you can inspect it........the valve and its handle are brass as i recall, and the handle and the actual valve are keyed alike with either splines or a "D" shaped shaft to mate with the valve handle, then secured with a screw......the shaft or handle may have worn, to where the handle itself is turning upon the actual valve assembly.....
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