Them wires are coming from you Stator,which is like a alternator on a car...You need to order the new connectors & replace then...Here is a website to get them from....
http://www.oregonmotorcycleparts.com...rs.html....The ones from this site are better quality then the cheap ones that are on there now....The stator runs the electrical system on the scoot & yes,it only puts out juice when the scoot is running,it is located in the engine....The battery is basically only used to start the scoot...Motorcycles run basically the same.....Good luck..