Yes, +12v from the battery to the horns should test them.

First trace the horn black wire back to the relay rather than the red wire.

The buzzer is activated by the key in the ignition and the door open and the buzzer circuit is separate from the horns circuit. I only mentioned wiggling the key with the door open because it is a very easy test and it is "semi-broken" in my '68.

I checked various '68 documentation that I have and other Firebird and Camaro forums and find no other standard horn relay '68 mounting locations other than on the radiator support under the regulator.

Is your '68 the convert in your Photobucket? Beautiful car! Coincidentally, we passed a '67/'68 white convert while vacationing in Germany in 1998. Going in the opposite direction on a divided highway, I didn't get a good look at it. I was just surprised to see a 1st Gen there and remembered it.