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Horn depends on which wiring system it's using. One has the horn button being the earth and the other has the horn being the earth. Check your horn, does it have a small wire which goes to earth, round by the coils or sometimes on the horn bracket itself. The black wire is the power for the horn and some other things, without that connected not much will work. I presume the new switch has horn/pass or just horn? Brown/white always seem to be for illumination lights but on the US model it's also used to power the running lights inside the indicators, that's the light blue/white and the orange/white. Brown/blue was the buzzer.
Mick has described it really well. On yours it sounds like the horn button is the earth. So the horn is getting power from the black wire near the coils, and when you press the horn button it earths out to the bars. If the switch isn't mounted on the bars there is no earth, have you been testing it with it off the bars?