That's an odd type of connector - it looks rather like a test point. I wonder if there is some type of BMW diagnostic equipment that plugs in there? I'll have a look on my car when I have the time, and see if there is a link from that connector to any of the fuse slots.
I did consider whether to get a dashcam with parking mode, but (in the UK at least) it doesn't seem to be a very useful function, because generally it won't capture the information that you really need to be able to use the footage as evidence.
In the end I came to the conclusion that fuse 65 or 127 should be Ok for my purposes - the power stays on long enough to capture any road rage incidents, but not long enough to risk running down the 12V battery while (for example) you're away on holiday.**
Having said that, I see that it's fairly easy to get "dashcam hardwire" kits that include a voltage monitor that will turn off the camera supply when the battery drops to (say) 11.6V, and that's probably enough to stop it from dropping too low for the car to power up.
[**Edit: Just noticed that the i3 has a 20Ah battery - this is a quarter the capacity of the battery fitted to my other car. Worth bearing in mind when considering how long a dashcam with Parking Mode will run before flattening the battery!]