Highly probable its the sender unit in the tank.. check to see if the float is fubbard..

 

Hi Phil. Thanks for the response. Sorry for my ignorance, but what do you mean by “fubbard?”
Is this something I can check myself, or will it need a visit to the garage?

 

On my Accent at about 1/4 left the gauge would stop dropping, and I would get a check engine light about the fuel level sender. It always would start working again on it's own all the way to empty and the light would clear with the next key cycle.

But here's what I did to try and 'clean' the sender pivot that apparently worked as it's been a couple years since any issues.

I let the tank get low to near the point it was happening, about 1/2 a tank. Then added a gallon of 50/50 lacquer thinner. It's the type that is toluene and xylene. Then drove around making quick steering motions so the gas sloshed around. Did this in an aggressive driving style out in the sticks. It was fun.

I've used the Lacquer Thinner before, about a 1/2 gallon in a full tank, and it really will give the fuel system a good cleaning and improve mileage/performance while it's in the gas and the next tankful.