There are two parts to the in tank sender, the float and the anti-slosh circuit.
The float moves a "dial" like the dash light dimmer, dial goes one way and dash lights get brighter, the other way they get dimmer.
The anti-slosh circuit, in essence, delays the dash board reading, so when you go around corners or stop and go suddenly the floats up and down movement doesn't cause the gauge to jump all over.
You don't say what year the B2 is so here are both OHM readings for the sender/slosh unit
Pre-1989 Ford, empty tank 73ohm, full tank 10ohms, 73-10 ohm range, so if you were to ground the sending unit wire going to the gauge it would be 0ohms so gauge would go to full, disconnect sending wire and you have infinite ohms so gauge would show below empty.
Full: 10ohms
Half Tank: 25ohms
Empty: 50ohms
Pointer Width Below E: 73ohms
1989 and up Fords, empty 16ohms, full 158ohms, 16-158 ohm range, opposite of pre-'89.
Disconnected sending wire gauge shows Full, grounded sending wire shows Empty.
I would test the sending unit again, make sure you are using an ohm meter that has a narrow enough range for the above, i.e. 0-200ohm
If you use an ohm meter that only has 0-1000 it would not read the changes very well as the range is to large.
Gauges do fail but it is much more likely that the sending/slosh unit fails, like the dash light dimmers fail, over time they get dead spots or just don't respond correctly