From this point everything was clear...
After rewiring, I checked the continuity with my ohmmeter and pushed the horn ring. Everything was ok... but...
I put the battery back in the car and tested the pair of horns...
Something very weird happened as... nothing happened... without the key, with the key, and in various positions...
I then wired directly the + to the fuse #2... My suprise was that I heard the gas pump running, as it's normally wired to fuse #3 as far as I understood...
Pushing the horn ring was successful, once... twice but afterwards the horns were even running continuously without pushing the ring...
I tried many combinations with and without any reflexion (just to see if it works...
), double checked every contact, wires... even removed the horns from their bracket in case it was running permanently the negative pole... but nothing good at the end of the day. I couldn't make it run properly
I rechecked again and again... without the battery everything works perfectly with my ohmmeter. Since I put a source of power, nothing happens as normally I guess the horns are running without the ignition key turned. When I connect the + to the fuse #2, then I can push once or twice the ring, the horns runs ok, but then for some reason keeps running without touching the ring...
So I'm puzzled and very disapointed, cause I thought I could solve my issue easily...
Another "funny" stuff is that when I turn the key as if I wanted to crank the engine, the horns briefly runs...
I'm not enough an expert to solve it by myself... I guess it's a small stuff, at least I hope...