The black wire at the horn relay should go directly to the two horns. Applying 12v to the black wire at the relay should be the same as applying 12v to both horns -- if they are wired correctly.
If there's 12v at the red horn relay wire, grounding the horn relay terminal with the green wire should cause the relay to trigger and activate the horns
If there's 12v at the red horn relay wire, grounding the horn relay terminal with the green wire should cause the relay to trigger and activate the horns