I think I might have found the issue for my car. Typical symptoms, i.e. lights turning on when pulling the keys regardless of the stalk's position, battery draining overnight, etc. Everything started after having the screen replaced, as usual.
I had the bypass wiring fix done by a car electrician so I lost the automatic lights but was able to go through the MOT. However the problem reappeared roughly a year later. This time I had to pull the relay to avoid draining, but then one day I came home with the rear lights on (feebly) and the horn's relay clicking away. Odd. I thought it could have been the anti-theft unit but that uses a separate horn/siren IIRC.
Anyway, this time I decided to check the windscreens even if there's no trace of condensation in the fuseboxes, inside or outside. I then checked the windscreen defroster (the wiring that stops the wipers from sticking to the windscreen) and although the wires seems ok, the socket was wet and had a little oxidation. I blew the water off, sprayed some WD40, dried it and left it unplugged but wrapped with a rubber glove's (middle) finger to make it waterproof. No problems so far regardless of the torrential rain we've had overnight.
See pics for the area involved, as well as the plug after cleaning it. One thing I noticed is that the cowls' draining slits in that corner don't have a mesh like the others, but I don't know whether it's intentional.
I'll keep you posted.