I just went through that same problem.
checked fuses, looking a wire diagrams etc...
I changed the fuel/oil/temp gauge a few days ago because it was weeping oil, with a used one clean one out of a 79 240D. like it because it is not in metric, but good old American.
as far as the center cap being shinny, I popped it off and painted it black, so it all matches.
I pulled the inst. cluster out thinking I didn`t connect something, and some white powder fell out of the left side.
(no that isn`t where I keep my stash)
I turned the rheostat (potentiometer) and it was all crusty inside with this white powder, probably from moisture? so replaced it off the old gauge and all fixed.
a new one is $93.00
from Fast Lane.
Using a jumper across the two pins, might be better to crimp two small barrell connectors to a short piece of wire and push on than solder a wire on. you might want to replace with a rheostat some day. PNP has a supply of these.
Charlie