No horn on the 66 Barracuda
Looking at a 66 horn button it look like a 67 up .
I suspect part of the horn button contact is supposed to be grounded and only when the contact leans to one side does it actually make a path to ground to honk the horn
On 67 there is a jumper from the column to chassis ground. Maybe yours is missing
I doubt that the ground path should be using the steering shaft or steering gear.