What year is the motorcycle? The Kawasaki dealer may have the horn button assy. Partzilla is showing that they have a horn button for the 81 KZ305-CSR & the photo shows that it includes the spring.
The horn has a power wire to it, usually brown, & pressing the button completes the circuit to ground. I think it's grounded via the handlebars.
I believe the passing button affects the headlight & I think it's a European thing to let a slow driver ahead know that you intend to pass. I think in Europe the headlight is normally off & pressing the PASS button turns on the headlight. There is also a separate headlight switch to turn on the headlight for night-time driving. Additionally on Euro models, there is an extra/separate "city light" in the headlight bucket that's kind of like a daytime running light. In the USA the headlight is always on when the ignition switch is on, but there isn't a separate "city light".
1981 KZ650-CSR. Competition, Sports & Road.