Dammit. Took it for a proper test run and it broke down after a mile or so. Battery completely flattened. Charging it up, so I can get the little bike back home.
Parts of the wiring are a bit messy from the previous owner. I gave it a "new" loom and that's fine, I rewired the rear part of the wiring. It looks like I'll have to rewire the electrics to the alternator, maybe replace the rectifier and check the alternator is putting out juice.