I have found the issue. Wait for it... That's the mystery thing you wouldn't suspect.
But in respect to the long extensive answer you wrote I've read and understood the logic. Thanks for taking that time and your patience for explaining those rather abstract diagrams to me. Much appreciated. I wish there would be more helpful people like you on FB / in the forums.
So now, I was about to pull the car out of the garage with a forklift truck, then push it on a lift (not sure of the word). The plan was to test the alternator by disconnecting the + wire on it. But as you mention there would be another way.
I was already imagining myself struggling removing the thing and replacing it. I've looked the prices and some how to videos yesterday and it didn't look as simple as I expected (I'm used to work on Z32).
But just before, I have heard that sometimes shorts can happen inside the battery... So you now what happens next. I test with another battery, no short, the car starts like a charm.
I would not have bet one dollar on that damn battery because it seemed ok, powering interior lights and the parking lights when connected to the terminals. The issue only happened when the brown wire was connected so you would logically suspect something down that line. Like you and I did.
Anyway, that's the first time I see that. So does my father. I'm glad to avoid a possible big bill at the dealership and simply have the possiblity to run again that car I was about to hate. But at the same time this is infuriating to have spent so much time on this and finding finally that's a so simple thing (I did a lot of tests before finding the brown wire, including a lot of harness parts, fuses and relays as I haven't the electric diagram).
Anyway, thanks again for your help