My 1863 cub will start everytime you try to start it but shut off after 2-5 seconds. I pulled off the line from the fuel pump and cranked the motor fuel is pumping to the carb. I blew out the carb, put a new fuel filter on. But it still does it.
The 1863 has a Kohler CH in it. The carb has a fuel shut down solenoid that needs 12V to open it. During cranking it gets power from the starter circuit and when running it gets power from the alternator. I'm wondering if you have a bad connection someplace. If you pull the air cleaner base you can get to the red wire on the solenoid, I would try a jumper from the battery to it and see if it will continue to run. Reason I'm going down this road is you say it will start and run for a few seconds so I think the solenoid is working but not getting power after it starts. I'm not on here very often so if you want to get me shoot me a PM. Hope this helps.