Welcome to AF.
Based on what you are saying it sounds like you have a problem with the horn ground in the steering column. All that happens when you press the horn button is a ground is supplied to the horn relay. The other side of the horn relay coil is hot at all times. The problem is you will need to disable and remove the airbag assembly along with the steering wheel to do further inspection. The ground goes through a slip ring assembly to transfer the signal due to the rotation of the steering wheel. It is not a solid wiring connection.