Thanks very much for the replies. I tried turning the wheel all the way to the left and pressing the horn, and no sound. The all the way to the right, nothing. Then I tried pushing it toward the dashboard, nothing. Pulling it away from the dash did nothing as well.
I guess it could still be something to do with the contacts in the wheel but it seems unlikely.
I mentioned that the horn worked after doing a clutch job because that seemed very odd to me. The horn had not worked for about 5 years previously so I thought there might be a connection (though I can't imagine what it would be).
Is there something somewhere else other than the wheel that could be causing the problem?