As the old saying has it, 'a picture is worth a thousand words', as it does in this case.
You haven't realised that, in a magneto ignition system, the coil is not just a transformer [as is the case in a 12V fed Kettering type car ignition, for example].
It's also the generator, that supplies the electrical power for the spark.
Basically, the flywheel has permanent magnets mounted in its periphery, and as these pass by the coil and the laminated iron armature that forms its mount, the changing magnetic field induces an electrical pulse in the coil's primary winding. This is then transformed in the secondary winding to a high voltage pulse, that is capable of creating a spark across the spark plug's electrodes.
So for this setup to work at all, the coil has to be mounted up next to the flywheel, with the correct air gap between the armature poles and the flywheel magnets. Bolt it back up, and see what you get!
As others have said, the cutout switch is the major source of ignition problems here.
