Hopefully this helps somebody because I couldn't find any info on this runaway condition.
Drove 1/2 mile to the gas station and when I started up to leave the starter stuck on. Turn key off starter is still running~! Limp it home wondering what the heck to do, get it in the garage and pull the negative battery terminal to get it to stop. Whew, WTF?
Calm down and start checking things, starter is hot of course but nothing is smoking and nothing smells burnt. Pull battery cover off and start checking wires from battery to relay and relay to the starter. OK good nothing is hot, nothing is crispy and nothing is melted. Probably smoked the starter though. If this had happened to my wife and I wasn't around the machine would have run until the battery died and probably melted down/burned.
I'll get to the point to save you folks some time and trouble. Because this is a kymco machine you need 2 different Kawasaki parts to make this repair, and information is scarce to say the least. The switch and a sub harness to connect it to the machine's plug.
Everything works now, but the starter sounds horrible so I'll be changing that too before spring.
Good luck out there and hopefully this is just a freak occurrence, but if I were you I'd get rid of this kymco part and put the Kawasaki replacement in now.
Switch, Magnetic is part number 27010-0767
Sub Harness Start Relay is part number 26031-Y034