If it was designed correctly(and all the buzz says it was) there is no reason this setup can't easily run a full electrical system just like a motorcycle. A dedicated lighting coil like this is the best way to get reliable power.
I remember WAY back in the day, I met a kid who had a very similar setup on a Kohler bb crank gokart engine built by his engineer dad. It had FOUR full size KC offroad lights on the rollbar and that sucker would scorch paint at 10 feet.
It DID sap a noticeable amount of power from the 12(originally)hp engine, but worked like a charm. He had full lights like any car including electric start with a motorcycle battery.
Your system looks very similar, so there's no reason you can't really go whole hog if you choose.
You just need to do some research and design a proper circuit.