well we have to decide if it is fuel or electroics.
Get a can of carb cleaner because it is more gentle on the engine.
Put short shot down each plug hole & crank the engine.
If it fires right up the timing is OK
If it backfires on both cylinders then timing is off
If it backfires on one cylinder the valve timing is off.
Repeat down the carb throat.
If it starts & runs, keep giving the engine SHORT shots for a minute or so.
If you can keep it running then you have a fuel supply problem .
If it backfires through the carb then you have a stuck valve or loose valve seat
Ditto for the exhaust
If it ran fine on the carb cleaner then rig up an alternative tank, off a push mower , motor bike anything and hook it direct to the carb holding about 1' r more higher.
Engine starts & runs fine then your problem is between the carb & the tank
Engine does not run then it is in the carb.
make sure the battery is fully charged because a low voltage ( 6 or less ) will cause the fuel solenoid to shut off .
The solenoid is a standard UNF thread so can be replaced with a short bolt ( for testing purposes only ) .
Runs fine with the bolt then the solenoid is at fault ( wireng also suspect ) .
Fairly common for debris that is floating in a tank to get sucked down int the outlet when the engine is running and cutting off the fuel supply then when not running the debris floats away and the tank flows fine, for a while .
Get a pair of red in-line spark testers and fit a them to the mower, run till it stops then check for spark .
No flashes means electrical fault you can leave them there I regularly find one that I left behind a year on more on a customers mower .
Dud safety switch can vibrate to make or break a contact thus a random no run situations and wires can break at the terminal crimp so they touch for a while then eventually break contact & you stop .
The kill wire to the coils can often get a bare patch so it randomly cuts the spark so after checking that the cut off solenoid is working so you can stop the engine, remove the wires at the coils and go mow.\Problem goes away means there is a short in the wire or one of the safety switches.
These are a PIA to find because it is a ground circuit so it does not blow fuses , let out the smoke or spark to tell you where they are.
No particular order to attack this you are just trying to eliminate potential problems, ONE AT A TIME. to home in on the guilty party .
