no experience with f650 but the fuel circuit is simple, there is power being feed to the float in the pass fuel tank, and when the tank runs down the float attached to a switch now sends power to the low fuel light, which in turn sends power to a relay (automatic switch) which will then apply power to the fuel pump on the drivers side and turning off the pass. side. getting to the problem at hand you said you have a problem with the light not coming on so that mean you need to check the wire at the tank for broken or wires that have rubbed through there casing and grounded which would cause the relay not to operate check your wires and as for the gauge showing full or empty that is a different circuit so it should not be affected hope this helps, and don't know the wire colors will see if i can find more info
02 F-350 Reg Cab Auto Trans L2 Blue, Marinco Mod, ZooDad Mod, Bilstien HD Shocks, Ford Alarm Code 3 Remote Start, Energy Suspension Spring Bushings and SwayBar Bushings, 2500 Watt Inverter, Sirius Sat. Radio, (Hardwired), Garmin Nuvi 250 (Hardwired), Blue Sea 6 Circuit Fuse Panel X2, Western 8' Pro Plus Ultra Mount Plow, 08 Taillights, Stancor Mod, Ford AIC, AIH Delete, Stainless HPX, Foil Delete, 05 PTM Tow Mirrors, 05 Upfitter Switch, 05 Center Dash, Federal Signal Smart Siren with Signal Master...