The reverse switch is also called the gear control switch (at least on the ML320) This part it shares with W210 series part No W210 545 13 32. Its deep under the shift. Best to get a pro.
The switch is on the side of the transmission--easily accessible and removed with two Allen head bolts. There are several sets of contacts inside. There is a resistor network which tells the computer which gear position is sellected. There are also some relay-style contacts which activate the backup lights. These are the ones in the picture. Water can enter the switch over time and corode the contacts. I took my switch apart to fix a problem with upshifting caused by bad contacts in the resistor network portion. You may be able to clean the heavy contacts for the reverse light. Stiff paper such as used in business cards is a great contact cleaner (you can also spray the paper with contact cleaner spray to help). Put the paper between the contacts and squeeze them together and rub the paper against them. I believe the switch is held together with rivets which can be drilled out. I replaced mine with small Allen bolts, possibly 3mm, and drilled/tapped the switch case so it can be taken apart in the future.
I believe the switch can be purchaased for about $40--the easy route-- but I like to fix things!! Also try reseating the connector on the side of the switch several times. The connector has a rotary latch on it. If you remove it from the trans it will have to be readjusted--you will notice the switch pivots on one bolt and the other mounting hole is a curved slot which is locked down by the second bolt. This assures that in any gear the appropriate contact is closed.