I totally agree with rwmastel, it is very improbably that the fuel gauge at the instrument cluster or it’s connections are bad in any way as that part is not removed often during the lifetime of the car.
The culprit in my opinion are the cables on the connector at the fuel sender that come from the wiring harness.
In many of the harnesses I have restored those cables are compromised, specially if you got the type with aluminum conductor. In some years I am not sure which ones Mercedes used for small gauge cables 0.75mm2 aluminium or copper with a solder coating which happens to get easily oxidized, making cables brittle. If that is your fortunate case you have two options:
1. Carefully cut and peal cable ends at the fuel sender connector.
Sumerge them in a solution with citric acid for 2 hours or more until they are in bright copper color. The solution should be warm to be more effective. If they are not clean enough use a sanding paper in grit 240 and carefully polish them (they are too brittle). After this is, proceed to solder each cable to the connector pin again. Use soldering paste from Radio Shack ( RadioShack Rosin Soldering Flux Paste, Non-Spill - Made in USA - 2 oz. Jar
https://a.co/d/0dCfEcu ). Also use a quality solder wire, since it makes a great difference ( Kester 24-9574-1402 K100LD, Lead-Free, Rosin Wire Solder.031" Diameter-Low Cost Alloy, 1 LB Spool
https://a.co/d/8Q54mx2 )
The second option, is…
2. Replace wires that bring signal to the fuel gauge in the rear harness loom. (Better and definitive solution)
This one is the most recommended. You will have to replace only two wire all along. The Blue/black, and the Blue/green. Use high quality wire with full copper core. Here some examples at Amazon. Ancor Marine Grade Primary Wire and Battery Cable
https://a.co/d/7dlsqaI Cable size is 18AWG. Buy Blue, Green and just in case also brown to replace the ground feed wire. 25 feet are more than enough each color.
Best regards
L.peterssen