I did a test last evening on my Audi A4 (no Start/stop but nonetheless...) B6.
It has a fuse for ECU powercontrol and something to do with the ECU itself. Couldn't find a diagram on this model online, so take it for what it's worth, however...
If i powered my Blackvue DR650S-2CH over this specific fuse for the ECU powercontrolling, the battery power would be dumped, almost instantly. The ECU seems to "signal" that "something is going on, i need power." So it instantly went from 0.1A (running idle) to almost 20A (19.6A) (fusecircuit max. amperage)
I believe your camera is hooked into a system critical fuse, that's not intended to be connected to that.
Try using radio or wipers, maybe indeed if installed, the heated seats (that fuse will be an always-on fuse).
Be sure not to choose something critical; Airbags, brakes, horn, blinkers, safety equipment like ABS, ESP, specific sensor-equipment for laneassist and so on.. Radio would be fine, wipers should be fine, if you got a fuse-socket for compartment-lightning, door-lightning or even 12V socket fuse, use them, and do a trial&error search.