I just keep thinking about the bumper sticker: "Horn broke - Watch for finger"

I am not sure on your vehicle, but many horns are wired a bit different using something I always called "ground side" wiring(I am not sure that is the right nonmenclature). Anyways, the ground side of the circuit has the switch instead of the "hot" side. I understand this is actually becoming more common even in American vehicles.

This makes us Americans who are used to hot side switches crazy when we test because you will have 12 volts at the horn all the time, but of course you usually only test when someone is mashing the horn so you think everything is fine all the way to the horn so it must be horn or ground. Not so in ground side switching. Your switch can be bad, wiring back to the switch can be bad, ground splice can be bad, etc.

Just something to keep in mind. Hope it helps,

NCDiesel