Hi, James; The problem could be the gauge, itself, or the fuel level sending unit inside the fuel tank.
Most likely, it's the sending unit. Electricity is my weak point, but I would advise against adding the resistor. I know it's a lot of work, but the best way to check the sending unit would be to remove it from the tank and check resistance there. You'll have to do that, anyway, to replace it. Or.......use your trip odometer and add fuel after so many miles?
So I have a Mercedes C180 Avantgarde 2013
When ever I top up fuel the gauge will show me its 1/4 full no matter how much I top up . Wanted to check the resistance by add a resistor to increase/reducing the level on the gauge in order to do a sending unit check. But my there are a lot of wire connecting to the fuel pump hence hindering me from doing. Hope this picture will help to identify the 2 wire that i should work on. Image