I suspect that the sending unit has a defect and is originating an out of range signal to the instrument cluster logic board or body control module. I do not know what electronic device is interpreting the fuel sender signal but I think the sending unit has gone awry.
My reasoning behind this guess. In Oct 2010 the electric fuel pump failed on my 2003 Neon. Odometer had 160,000 miles and it was the original pump so I deduced that it was about time to replace. I purchased an Airtex pump through RockAuto.com. As has been the practice since the early 1990s the fuel pump module contains filter, pressure regulator, electric pump and fuel level sending unit. I replaced the entire fuel pump module.
After about 2 weeks of driving with the new, replacement pump I noticed that upon filling an almost empty fuel tank that after turning on the ignition it would take 5 minutes for the fuel gauge indicator needle to move from the empty range to full. That was very bizarre behavior since this slow rise to Full never happened with the original factory issue pump and fuel sending unit. It would not always be slow in rising after every fill up but would do it periodically. The fuel gauge level seemed to be accurate so I decided to live with the odd behavior.
After about 4 months I noticed that upon filling the fuel tank with gasoline, the fuel gauge needle would rise to the 3/4 mark and then stop moving. I knew that I was getting the fuel tank full so I was starting to suspect something was wrong with the resistance strip on the float arm. And the negative comments posted on this forum about the lack of quality in Airtex pumps only reinforced my suspicions. Since I was still within the one year warranty on the pump I decided to replace it.
When I removed the pump I used a volt-ohm meter to check the resistance of the sending circuit with the float arm down (Empty) position resistance was around 100 ohms. That seemed to be on specification. With the float arm fully up (Full) position, resistance was over 1200 ohms. Specification was around 980 ohms.
The analog resistance reading is sent to a logic circuit (instrument panel board, body module, etc) and is interpreted and converted into a digital signal value. That value is used to drive an electric motor that turns the needle gauge to the proper position. My theory is that the high resistance reading was way beyond specification. Logic is built into the needle gauge driver motor circuit such that if an out of range value is expressed, the motor is protected and either slows its movement which caused the slow movement from empty to full on the gauge. Also with out of range value the circuitry will not allow the needle motor to extend its full travel. This protects the motor from damage.
I received a replacement pump from RockAuto.com. I checked the resistance of the sending unit float arm in both the up and down position (Full, Empty) before installing the pump and it was within design specification. After installation the fuel gauge has behaved normally. After fill up the needle gauge moves immediately from Empty to Full and the needle will move to the Full position on the gauge.
I know this sounds a little weird but it is what I experienced. So if you can get a dealer service department to use a factory diagnostic scan tool to check the resistance of the fuel sending unit circuit when the fuel tank is full, it may show an excessively high and out of range value.
If you have a video recorder, you could make a video and show how long it takes the fuel needle gauge to move from Empty to Full position. Maybe then a dealer service department might believe you.