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.
Good luck.