1. Brake light operation is subject to manufacturer's whims and logic. VW brake lights work w/ or w/o ignition on, Mercedes, in my experience don't.

2. There is not likely a fuse for that 3rd brake light. Most likely it is wired back to either the left or right side taillight and just gets power from there. Look at the color of the wires where they connect to the 3rd brake light and see if you can find the other ends of those wires at the connector at one of the taillights.

3. I would first suspect the wiring harness that runs up along the trunk hinge. Opening and closing trunk lids over the years will actually break the wires in the harness. This is not an unusual problem.
You could also have a bad connection at the light on the trunk, or at the taillight where the 3rd brake light is connected.

Hope that helps.

__________________
Fourings

84 Audi Coupe GT with Turbo engine, EFI (buh-bye CIS), Jamex seats, Koni's/H&R's, e-code lights. 210k and counting.
1992 Anthracite 400E, 161k, "Grey Ghost".
1986 VW Quantum Syncro, 192k, gone to the crusher in the sky.
1989 300TE 172k. (Was mine, now also Mom's car)
72 280SE 4.5 (Mom's car)