First issue is that you should not see 12 V on both of those contacts. In your first post, you said you measured full voltage at both, but it should only be on one.
So that seems amiss right off the bat.
You can test the horn by running a power wire directly to it. If it honks at that point, then you know that the horn and its grounding point are still good.
You could even do that at the firewall connectors, and at the steering column connectors to keep tracing things and narrowing down the prospects.
Since it worked before and you’re seeing 12 V on both, seems to me there’s a good chance that some of the wires have become frayed and shorted inside the steering column.
But that would be the last thing I would hope for and try to fix.
Check the easy stuff first.
After you get it all sorted out, I would convert the system over to a relay without a doubt. It’s hands-down how it should’ve been done originally.
It reduces the wear and tear on the contact points in the horn button and usually makes the horn louder.
It’s also very easy to do so.
Let us know when you get that sorted out and it’s an easy walk-through with a relay.