Russell,

The relay has (I think) three terminals. You have already identified one correctly, that's the power wire for the horn itself. That power wire is part of a normally open contact inside the relay. A small internal jumper grabs some of this power and applies it to the coil that closes the relay to power the horn. The relay coil has power, but is insulated and has no ground. The third terminal is that ground..which is completed when you mash the horn button down.

So you can see that there should only be voltage on the terminal connected to the battery...the power wire, not on any other terminals. The relay should do nothing when the connector is removed or attached.

I think the relay is toast. No terminal should have continuity with any other terminal except when tooting the horn. You are doing a excellent job troubleshooting and explaining these problems...keep it up. Sorry for the mini-novel on such a little relay.

PS..The horn could be in 'auto-toot'. Pull the wire that goes to the horn button then remove and reattach the power wire and listen for clicking contacts. If this kills the clicking, the horn wire is grounded somewhere and the horn is dead, or the contacts are burnt and not passing power to the horn.

Stuart