I had an early Bug with a Tecumseh engine and that was white. In the early days of Westwood there was a certain amount of making it up as they went along and “ use what they had”. It sounds as though what you have is a Dynostart – starter and generator combined – the two functions in one unit, not that unusual in those days when many of the engine manufacturers had not got around to incorporating an alternator under the flywheel with the ignition windings.
Sounds like your Bug is original, so many were butchered for lawn mower racing.
I’m only about ten miles from you, so if you need any help send me a PM.
Edit. I should add a word of warning. With any electric starting system it is very important that when” messing” with the wiring that you don’t end up sending battery voltage up the ignition stop/kill wire to the ignition windings – it will burn them out in a millisecond. So if you are experimenting sorting the electrics out my best advice is to disconnect the kill wire until you are sure that all is in order. You mention smoke – hopefully that has not already happened.