The wiring of a petrol or gas scooter engine involves a few fairly easy steps if all the necessary parts are in place. Most combustion engines that run on gas also incorporate a flywheel and electrical generation system, also known as a stator plate assembly. The stator place is already pre-assembled with the necessary coil-wrapped magnets that generate electricity as the flywheel magnets spin around them in a circle. These parts then attach to wires that stick out of the engine. The only remaining task then is to connect the engine wires to the scooter.
Locate the wiring coming from the flywheel and stator assembly on the engine. Pull the wires gently so that they are fully extended from the engine as far as they will stretch. Check the wiring insulation for any damage. Wrap the individual wire area with electrical tape if damaged. Cut the tape end with scissors for a clean tape cut. Don't pull it apart -- the tape will stretch and deform.
Strip the wire ends ¼ inch if they are missing wire connectors. Press new wire connectors onto the bare wire ends with the wire crimper/stripper tool so they can connect to the appropriate scooter wire. Attach male or female connectors as appropriate to match the connectors on the scooter wiring.
Insert the engine wires with their new connectors into the junction box that is already attached to the engine -- most scooter engines come with a junction box to avoid the wires being pulled while riding. Match the wire colour from the engine to the same wire colour from the scooter wiring. Connect the male and female wire connectors.
Use a wiring diagram for your model scooter to track your wiring connections correctly. Many are posted on the Internet to download for free and some even come in colour-coded version rather than black and white diagrams.
For a more permanent cover of a wire that has a crack in it or bare spot, you can use shrinkwrap tubing. Place the tube section over the bare spot and heat it with a lighter. The tube will shrink tight around the area you want covered when heated. Just be careful not to burn it.
Be careful when using a soldering iron to repair broken engine wiring if you need to do such work. The iron tip is hot and will immediately burn skin. The fumes from the solder are also toxic to breathe.