Or just install a real gauge and know what is going on.
The stock sender is 4 bucks at the local parts store (not sure how much a Motorcraft sender is, but with how the gauges are calibrated, I dont see the need for a 'precise' sender).
Make sure the sender wire is not pinched or chafed (a DMM set to ohms can help determine this). Easiest to throw 4 bucks at it with a new sender first.
take the sender signal wire and ground it,this will max the guage past hot to let you know if the guage still works.If it doesnt move,either wire problem or bad guage.