i dunno about the 201, but on my 123 it was a matter of removing the
wood panel around the gear change.  the switches themselves were fixed
into the wood panel, so i wouldn't try pulling them out.  if i remember
correctly, i used somethign alogn the lines of isopropal alcohol, but i
doubt it made a significant difference; it seemed that just getting
things apart managed to put whatever it was right, though i did also
loosen one sticky witch at the same time.... who knows.  anyhow, sorry
that wasn't more detailed.  good luck, and do try not to crack any of
your wood trim.

I did NOT take apart then put the switch back successfully.  Maybe you
have better luck.  Many W201 are old enough and they show up frenquently
in junkyards.  Try switching to another one (even switching the two you
have on the car) can prove whether it is bad.  If you are near
Washington DC area, Potomac German Auto sells old switch $1 a piece.
That is where my spares come from :-)

By the way, I have an 84 190D too (around 250k miles)