I am thinking it is out of time. Spark plug wires reversed? Other timing issues? I saw this happen on an old pickup truck in 1976 when one of my employees took out the distributor to install new points and re-installed the distributor 180 degrees out of phase.
But highly unlikely if not impossible to happen on a lawn mower.
Only the old engines that were horizontally opposed typically had a coil with two wires coming out of it and even then they designed it sometimes so they wouldn't reach to the other plug but in reality it probably wouldn't have mattered much. Lol
Most of the ones like the v-twins all have two individual coils so you certainly couldn't reach the plug wire to the opposite side because it wouldn't be long enough.
Typically if you can see any spark at all, or if it will tickle your fingers when you spin it by hand a little bit which I don't like to do because I hate to be shocked, then it's fine spark wise.
The next thing to do is always give it an external fuel source because about 9 plus times out of 10 it is not getting enough fuel so I always start there instead of starting a spark.
If it doesn't fire that way or if it pops or does anything odd then it's not a bad idea to check the flywheel key but I typically just pull both plugs out and stick my finger in the hole and spin it over to make sure it goes puff puff puff puff puff and then it never sucks my finger in the hole or does a double puff or irregular pattern etc.
So out of the few that it's not fuel related from my first test, I'm able to determine that it's a cylinder compression valve problem by the second test because either I will have no compression or it will try to suck my finger back in the hole which means the valves are not closing properly for the no compression or when it sucks your finger back in it means the intake isn't opening so you probably have rocker arms loose or hanging there or been pushrods etc.
Another option on the one cylinder without compression is that the Piston isn't moving up and down from a snapped Rod so you want to look in there with a flashlight or stick a straw or something in the hole to make sure you can prove the piston is going both up and down repeatedly.
This diagnostic procedure will lead you to the problem over 98 times out of 100.
Now fixing the problem of why you may not have compression in one cylinder or why it may be sucking your finger in and not opening the intake valve is a different matter but that normally does not involve removing the head but most people's first step is just start yanking things apart and pull the head off when it's not even necessary.
Another good percentage go out and buy a new head and waste somewhere between 85 and 185 when they did not have to do that at all.
If you do find that push rods, it is highly unlikely to fix it by putting new push rods in because most likely they will bend immediately on spin up because typically that is a slipped valve guide which is preventing the valve from moving far enough when the rocker arm pushes on it and the weak link is the push rod when they have aluminum push rods. When they don't, it often tears the rocker arm.
As you can tell, I've seen a lot of these. Far more than I wish existed because it's just shoddy execution of a fairly decent design and situation but they drop the ball at the end making things durable enough by simply pressing valve seats in and valve guides in and not using loctite or a lock washer on the rocker arm studs into the head and simply not making the valve train adjustments and fasteners durable enough to hold things in place without vibrating loose.
This is different than the head gasket blowing problem on the Briggs which is a design flaw and not execution of the assembly.
