Thanks, that was my hope!
I already found the connector in the service manual – thanks to @raymo –, it's what's in the tweezers in step 23.
Then again, looking at all those steps before step 23 (ok, I obviously can leave the battery alone), the disassembly looks more complicated than I would have liked...
Which made me try something else right now, before starting the disassembly: applying substantial pressure with my thumb on the back cover at the exact place where that connector must be underneath.
And what shall I say, for the time being the camera is back working! 🙂