Not exactly sure on the actual construction, I'm more of an electrical guy. As for wiring, there are many ways to do it. If you didn't want to deal with a battery, you could get one of those extension cords on a reell, so when it was heeled back, the extension cord would wind up. You'd have to mount an old computer power supply or large transformer on the assembly to power the lights/horns.For wiring the lights, have a separate switch for them, and a momentary switch for the airhorn. I would suggest getting an electric air horn (is there such a thing?) because you aren't dealing with compressors. Wolo makes one that has an airhorn and 3 siren tones (don't impersonate a cop now) for a little over $20. It also a includes it's on switch box.
As far as relays, you don't really need them I don't think. Just wire both + on the headlights together using a wire nut, and make a pigtail to go to the switch.
If you need any more assistance, PM me.
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