We need some pictures of the ride-on and its engine to be able to help you with this.

As background for members, the Honda HT4213 (42" cut, 13 hp water cooled GX360 twin cylinder in line engine, OHC driven by rubber belt) was made from 1987 to 1989. A horizontal crankshaft water-cooled engine in a ride-on is unusual enough to be interesting. The engine looks as if it was designed by car-engine engineers: it is complicated, heavy, and looks very difficult to work on without the shop manual. The engine alone has a more complicated wiring diagram than most ride-ons.

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Here is the HT4213 owner manual:
http://powerequipment.honda.com/pdf/manuals/31750803.pdf