Why the 3rd back light out, tunk want open, light plate light out.

First off, the sound you mention may be the "ka-tunk, ka-tunk, ka-tunk" sound related to the vehicle vapor recovery valve under and in the back of the car related to vehicle fuel tank vapor recovery. This electro - mechanical valve operates while the car is on or off.

During time when you can fully open the hatch, Start by cleaning the rubber seals all around the hatch with a silicone treatment to prevent sticking.

Spray a lubricant that will not harm paint into the 2 hinges inboard of the upper struts. Spray some lubricant onto a paper towel and rub down the shafts of the struts as well to remove any glazing that may have built up.

Inspect the exposed paint areas of the hatchway and the hatch itself for signs of scuffing which may validate intermittent heat swelling of a tight space requiring panel realignment.

The following can be dangerous so have a qualified mechanic;
Inspect the installation of, remove and test the function of the struts to eliminate a source of binding. The end of the strut with the rounded cap attaches to the car body.

Have a body person inspect the installation of the outer rain seal at the closed top of the hatch. I had a shop owner ask to inspect mine years ago as they couldn't see how it installed on a car they were repairing. Could be a source of hang up.

Hopefully, this helps.

Take the signal from one of the door switches. They are normally open switches that close and complete the circuit when you open the door.

You have to remove the unit and it is two screws in the tunk

Have you check the globe or fuse?

There is a sensor in the latch assembly usually. The whole thing may need to be replaced. Try spraying WD40 in the latch and opening and closing the truck a dozen times or so. Shut it pretty hard. Sometimes that will do the trick.

The plate lights are connected with the park lamp circuit and it is Possible that the GROUND connection to the ligh assembly has failed or it can be the lamp holder that has failed.

CLS550 2010. Same complaint trunk won't open, third brake light and license plate lights not working. Two ground wires (Brown) were broken inside the bundle of wires right were the zip tie holds them to the trunk lid arm. When I first looked I missed them. Remove all the corrugated wire protection and look the wires over very closely. One of them was broken inside but the wire just looked kinked on the outside. The other was broken in too. 7/9/17

Means you have a taillight, brake light, reverse light, license plate light, or 3rd brake light out.

this is the way i do all my cars and trucks
take off the coil wire and the dist cap, take out #1 plug
have someone help you, place your finger over #1 plug hole but not in the cylinder but over it,
have your helper tunk the key and turn over the motor just a tunk as in maybe 1/8 of a turn keep tunking it until the compression pushes out your finger your at #1 so look at the rotor button of where it is pointing and mark it on the dist then put the cap back on and place #1 plug wire on the post where you marked it

i found the solution to same problem here.
http://mbworld.org/forums/e-class-w211/314638-no-power-trunk-3rd-brake-light-license-plate-lamps-2.html
it was a easy fix, broken wires in the boot a common fault with mercedes.