That thought occurred to me and I think my DVM has the ability to measure amperage draw.

However ... when you look at the mechanicals of the horn "button" it sure isn't designed to have any significant current flowing through it so its no surprise that there is a relay in the circuit. My guess is the horn itself draws no more than ten amps whereas the relay may only require two or three. And then of course there's a "staple" to complete the ground circuit !!