gjberche,
The wire headed to the horn button is the ground side of a very small relay coil. Not only does this coil take little to energize it, being on the ground side, I think most of the inrush is taken up by/through the small windings of the coil.
No big zaps with this little guy! This is the classic "small load switching a big load" kind of deal...just like your TV remote or your garage door opener.
Stuart