likes to quit

i have two 96 gators,early and late by the serial #.the later is the one with the horizontal muffler.it starts easy and will run for a long time as long as you dont idle it.when it quits it will not restart until it cools off.i have read several things that tell me that will be the igniter.it also will not turn off with the black kill wire in the harness by the crankcase hose.on my early one the igniter is on a small plate by that hose,on this one the plate is empty.
Thanks for any help.