There should be a relay in the PDC (the little black box under the hood). If you're lucky, it's just corroded a path to energize itself. Pull it and look. Swap it will another (there should be a few identical to it) and see if the condition disappears with the horn ..and emerges somewhere else.
If you're not that lucky, then it's a hunting mission. I'd be suspecting that water got into the horn switch with some dirt and is bridging out the contacts in the steering wheel. That's a bit more complicated with the air bag and clock spring. I've never had it off, personally.
I'd probably be playing like a chimp with a whiffle ball bat to avoid taking it apart (leaving the wheel inverted or other various angles - disconnecting the battery and spraying plastic safe volatiles in there - banging the horn area of the wheel ..etc..etc) ..but I'm lazy
Gary L. Allan, Sr.
If it ain't broke ..fix it 'til it is