Appreciate the pictures my guy!
When I did the install of my ear cannon horn, I was forced to use the relay due to amperage draw of that horn. Admittedly, I would've used a relay regardless, and I'll explain why.
I would always suggest using a relay for devices like this. If you use power from the factory wiring, as the wiring commonly goes like this:
power from battery, horn fuse, horn button, horn.
That path, due to its length, introduces voltage drop along the entire path. While 12v is the standard for horns, with a long power run you could only be getting 9.5v or similar at the horn(s). The result is a horn that is not at 100% volume when you hit the horn button.
Getting power from the primary power source (battery OR massive positive lead under the red cap), then to the relay, then the horn (the horn button triggers the relay, but does not supply power to the horn) is a far shorter electrical path with a lot less power loss. You will likely get 11.5v or 11v of actual power at the horn(s). The result is a noticeably louder horn.
Another detail. If you know the amperage draw (not volts) of the device, you'll want to get wiring that is rated to handle that much amperage, and a bit more if the price isn't significantly more expensive.
Ampacity is the maximum current that a conductor can carry continuously under the conditions of use without exceeding its temperature rating. Cerrowire's ampacity chart helps calculate the load requirement for a circuit.
www.cerrowire.com
This site shows the wire gauge and amperage it is rated to handle. Be careful of CCA (copper clad aluminum). If you have CCA, you need to use the aluminum rating, and not the pure copper rating.
If the horns only pull 5amps each, then 14 gauge cable would be fine.
if you're crazy and run this ear cannon, it comes with a 30 amp relay, you'll want to run 10 gauge at a minimum or 8 gauge (which I did) for a bit of extra electrical headroom.
This is a full-power railroad locomotive/ocean liner type compressed air horn squeezed into a bike-mountable package. Totally overkill, until you need to wake up some lethal driver.
www.aerostich.com