puzzling horn problem

THe horn on my 05 Aveo is dead. Troubleshooting so far;

fuses, 2, good
horn relay, clicks when horn switch pressed
Horn, hot-wired direct to battery and sounds
Horn wiring plug ( at horn)
tested as a circuit- dead
tested individualy to ground
Leg 1 12v+ always hot, no change with press of the horn switch
Leg 2 3v+ same

its this last part that's got me

I haven’t seen the horn circuit but from what you describe it sounds like the relay should be switching the ground.
Since you hear it clicking it appears your signal side is good but doesn’t mean the load side contacts are.
Test or swap the relay, and verify your wiring to the connector.

Cheers