That suggests to me that the third brake light wire is a black/pink cable coming from the rear sam pin 22
It is not protected by a fuse as such but electronically, almost certainly by a current sensing foldback circuit. That circuit is probably also used to indicate the unit (third brake light) or circuit failure.
If it were me, I would probe pin 22 with a testlamp - around 5 watts with the brake pedal depressed.
If the testlight illuminates then this would suggest the sam (and associated brake light switch circuitry) are ok. I would then trace with the testlight from there to find the break in the circuit - with the wiring around any moving parts e.g. the boot hinge being the most likely culprit.
If there is no output from that pin AND the brake lights illuminate, I would suspect the sam - practically the only way to test this is by substitution.
If you do find current being supplied to the light unit, it is then worth testing that there is a good earth.
Just fyi, my own experience of testing a light circuit on a recent Mercedes is that you will see the circuit ‘pulse’ if there is no load (bulb/led unit) connected. My assumption is that this is how the circuit detects if a load has been re-established. Not easy ro detect on a digital meter, but more obvious on an analogue meter or my favourite - a testlight.