Fuel guage stays on empty and low fuel light stays on,no other problems

I suggest you read the vehicle owner's handbook to be certain what the exact function of the light is. You will need to know that in order to determine whether the light is warning you or is broken.

The fuel light usually warns the fuel level in the tank is low...

if the light works for low fuel it is not a fuse, most likely cause is a bad sending unit in the gas tank.

u either have a bad level sensor in the tank or the guage is bad. u need to get wiring diagram and find connector for fuel sending unit and jump wires to trick guage into thinking it is full if it still say empty u need instrument cluster if it goes to full it level sensor in the tank

A loose connection on the sending unit could cause the problem but also moisture in the tank in cold weather could also be a factor in which i would add fuel line antifreeze to a full tank of fuel..........Hope this helps you out.

The fuel pump float is on its way out . Pretty soon your gonna need a new pump.

• Full instrumentation pack (four ancillary guages plus tachometer) - with volt meter & oil pressure guage.
• Speedometer, odometer, tripmeter, fuel guage & water temperature guage standard in addition to the above.
• WARNING LIGHTS: High beam, rear window demist on, turn signal / hazard light, alternator fail, lights on, park-brake on, washer fluid low, radiator coolant low, cruise control indicator and low oil pressure.
• AUDIBLE WARNING CHIMES: low fuel, lights on, low alternator charge, low oil pressure, high coolant temperature and brake failure.
• Trip Computer standard featuring fuel consumption figures, distance to empty, average speed & time display.

I found this site, no mention of the fan in a cylinder, but I'll let you figure it out. Hope this helps.
http://www.trueblueford.com/ed_pages/EDfalcon_fairmont.html

I had a 2001 silverado 2500 h.d. with the same problems. I took it to a gear head and he found that the emergency brake cable was loose causing it to trigger the warning light on the dash. As far as the low fuel guage I took it back to the gear head and he found that the float in the gas tank was broken causing the low fuel light to come on. The float wasnt a big deal until I lost track of mileage and ran the tank dry.

or sending unit is worn or faulty

You need new fuel sender cards. There are two of them. They're in the fuel tank.

The only thing that will cause this is the gas guage sending unit.