When I fill the gas tank completely, the gage displays Empty. After driving approx. 35-50 miles it starts working and moves to Full.
This does not happen if I fill it 3/4 or less.
You have a dead spot at the top of your fuel sender sensor. The best fix is to replace the sender. Before you do that, you might try some of the cleaner that GM recommends, with a full tank of gas.
Unless you are prepared to drop the tank & pull the fuel pump, chances are that you will just learn to live with it. The sending unit & float are attached to the fuel pump so the only way to get to them is by dropping the tank. You can try dumping some kind of approved cleaner in the tank as it won’t hurt.
If you are one of the lucky few who have an access port in your trunk to get at the fuel pump/gas gauge sender assembly, then you don’t have to drop the tank.
It would be a good idea to tell us what make, model and year car you have.
I have you one better. Mine shows a low fuel light until it gets low, then it chimes the low fuel warning and the light turns off.
If anyone figures out why mine does that I would appreciate it. I have a 2002 VW NB diesel, ~ 120,000 milesI had the same problem with a Chevrolet Uplander. The sending unit in the fuel tank had to be replaced which meant dropping the fuel tank. Fortunately, my Uplander was still under warranty. This seemed to be a rather common GM problem on some of its trucks and vans.