I managed to do these tests with practically NO ACCESS to the starter nuts.
I was lucky enough to buy this tool at the supermarket :

The starter motor was a bit struggling( acceptable, considering those clumsy connectors I made for this task), but DID work.
As regards the selector lever switch down under, it is a real simple device, I mean just a few pieces of wire , no microchip, no anything....
I disconnected/dismantled it again, in order to check if there's a broken cable in it, no problem detected, it's in perfect condition :


I was even considering if overtightening of the seven small bolts might cause any problem....no, it does NOT.
Well, I also removed facia during the overhaul ( placing it back was a real "fun"

)...and I remembered some white device with a button behind the fuse box under the steering column.
I thought that button might "do something important"

....so I lay under the steering column and pushed the button :

I cannot tell you what I felt when trying the igniton key again ...and those ....cking lights were working as usual !!!

But then ....the solenoid "clicks", starter motor does NOT turn!
So I managed to escape the animals thrown at me by those French gatekeepers...but I'm still outside the castle !
What next ?