Check the wire that runs down through the steering column. If it's the original wire it could be worn through and is shorting out, causing the horn to blow.
It's pretty obvious that the horn ring grounding points are not keeping a proper air gap. Could be bent or loose. Only you have the ability to determine that.
You say the ring is a hair trigger. Well, that is your problem. It is misalined or there is not enough tension on it to maintain the proper air gap. Simple solution. Good luck with it.
I've heard of the horn shorting out and shocks your arm as your cruising down the road looking cool with your arm resting on the window trim....let's hope that doesn't happen .ha...ha
Randy