So, here is the final report.
Having analyzed the J363 and its socket, and having found no problems:
I guessed the problem was in the wiring, from Fuse 10 (which I knew was good and had 12V with ignition ON) to the Relay. So with this:
I was able to directly wire 12V from fuse 10 to the relay. At this point, the was online again. I posted the results of the autoscan to let you know I was 'on the road again', and started the engine.
I took the car to my mechanic because the MOT (annual test of vehicle safety) was pending.
Now the car is back, and I restricted the problem to the wire going from the fuse to the 6 pin connector under the dash panel. As per the diagram, there's a wire going from the relay to a connector (T6/4), and from there a wire going to fuse 10.
So I accessed this connector:
and found that from J363 relay to T6/4 the wire was OK. Good as I could remove the soldered wire from the relay inside the engine compartment, and now I only have a wire going from T6/4 to to Fuse 10. A short 20 cm wire which will stay there until I find the time to fix the broken connection, which doesn't worry me at all, I just need to remove the under-dash panel and have a look. Not a big deal.
Thanks thank thanks.
I need to go out now, further details later. I am curious to see the fault, and find out what caused it.