The controller's battery wires and motor wires are 14 gauge, and its other wires are 22 gauge.
We use and sell automotive grade primary wire for making wire extensions since this type of wire is engineered for use in vehicles.
For extending the battery pack wires or motor wires we normally use 12 gauge wire, and for extending the other wires we use 22 to 18 gauge wire depending on which gauge we feel is best for the particular application.
We are very particular about the wire that we use and sell and for larger gauge wires, we carry pure copper multistrand automotive primary wire with extremely abrasion and heat resistant cross-link polyethylene insulation. Our smaller gauge wires have vinyl insulation which is more flexible than polyethylene and we choose smaller gauge wire with a high copper strand count so it can handle repeated bending without breaking.
Please let us know if you have any questions.
The connectors for the throttle and controller are available on this page: https://electricscooterparts.com/whitewiringconnectors.html
For the reverse switch, we recommend using a switch that takes a little bit of effort to flip to prevent it from accidentally being switched into reverse when the vehicle is moving forward, and vice-versa. A good choice for this would be our item # SWT-95 toggle switch which is available on this page: https://electricscooterparts.com/powerswitches.html#toggle-switches
Please let us know if you have any questions.
Tim H