Couldn’t find a wiring diagram for that but judging by the parts list it’s very easy to figure out.
First off that kart originally had a Tecumseh motor electric start, battery etc…
That being said if your Briggs motor doesn’t have electric start it likely won’t run a light system, unless by chance it has the proper coil for lighting. Let’s determine that now before we go further.
Do you see any wiring / plug coming from under the fan shroud?
Usually a square plug with 3 or 4 wires ? I believe 3….been awhile
If it’s only one wire exiting from the shroud that’s your engine kill ( magneto ) wire usually black, engine is not equipped with a lighting coil.
If your motor has more than one wire then we can proceed , you will need a multi meter and know how to use it. From there I’ll be able to draw you a wiring diagram.