....which reports resistance at the sender, you might like to jimmy up an ohmmeter connection in place of the gauge and see if you get the same symptoms - an analog (needle) type would be far safer when driving than trying to read a digital one. Thus if you already have an ohmmeter, you save spending on a gauge which might end up being OK in the first place.

I do not know the 300E, but the gauge will probably be in much the same location as on my 300SD which is accessed after removing the rear seat back. The slider inside the gauge's tube brings varying lengths of wire into circuit, altering resistance as it does so, which is what your meter reads. Try dismantling the tube and cleaning the (very fragile) wires, ensuring that the puck/slider moves freely on them.

One other problem source can be a bad ground - check the connections (brown wires, lots of them) and clean/retighten when you pull the instrument panel.