I just installed that kit, and was deliriously happy about how easy it was, how well it functions and how robust it seems to be. Plus, the price is right. I replaced another brand that never worked right.
The additional wire runs to the brake, if your local laws don't allow for the brakes to initially sequence, or you don't like the initial, one time sequence when you push the brake, but I think the initial sequencing is cool, so left the wire unattached.
BTW, If you choose to leave the wire unattached, be sure to put some installation on it, or it will short out and that wouldn't be good.
Paint is a protective coating