Lumbergh - Just my thoughts based on your description that it ran fine for a bit, after sitting for a good while, but then bogged down/stalled after running.
This sounds more like a fuel supply loss issue than an ignition issue. It could be you have junk/debris in your tank that will naturally get drawn to the outlet of the tank and when there is enough of it, it can block your outlet screen. When the engine stops and suction on the outlet is removed, debris can drop off from the screen, temporarily restoring fuel flow until it gets drawn back when fuel flow resumes at engine restart/running.
An alternative fuel supply issue has to do with your tanks vented cap not functioning correctly. Maybe you recently replaced the tank cap with a repop (which are kinda well known not to vent properly) or your old cap vent has become clogged/obstructed. A non-venting gas cap will stop fuel flow after a period of time running as when the gas exits, air has to be allowed in to stop a vacuum from forming. With no or reduced venting, the vacuum created by the pump drawing fuel out to the engine will stop fuel from flowing to the pump/carb, starving your engine till it stalls.
The leave it for a while and it will restart/run for a bit description, sounds like the tank eventually sits long enough to allow air into the tank and temporarily remove the vacuum condition.
Perhaps an easy way to check if you have a venting problem is to release the gas cap from the tank and start/run the engine. If your engine starts/runs normally and doesn't stall/die, you've likely found the problem is your tank cap.
If that test doesn't resolve the bogging/stalling, you' ll probably need to further investigate your tank and fuel delivery system.
