If I understand the method you are checking this problem by, it sounds as if the contacts inside your horn are welding together or staying together from a mechanical problem (ie. damaged contact mechanism in the horn) or a magnetism effect until the power is released. I say magnetism if it does not come back on when you touch the hot wire back to the horn or hook the battery back up. Or mechanical (welding or interference) if you have to tap the horn to get it to stop. The contact arm that the contact is mounted to inside the horn is likely weak and does not break the contact after the wire is removed, but for this to happen there would also have to be something completing the ground connection from the above described problem.
Usually the problem is a contacting of the ground wire in the either inside the column or between the column and the horn, but this doesn't sound like the problem you have described.
