95 E420. Fuel gauge acting weird

[Brabo]

I recently bought a 95 E420. The car is in very good condition but it has a few minor problems. Some of them I have been able to solve by searching through the threads on this forum and finding the solutions and hints that enabled me to fix them.
However, one of the remaining problems is the fuel gauge in the dash. It tends to display a random fuel level that doesn't reflect the actual level. At first I thought the sending unit in the tank was defective, but just before I fueled up yesterday the gauge showed a full tank while the light for low fuel level came on to warn me. Now I'm not so sure anymore that the problem is still the fuel sender in the tank. Does anyone have experience with this phenomenon?

Thanks.