G'day,
your system is the older points and condencer system. i would almost bet that its the points giving you your trouble, becuase they get dirty and corroded easily. the first thing i would look as is the stop switch(if installed) and make sure its not too gunked up and there is no wires obviously worn threw or toughing. the easiest solution is to replace the whole magneto with a later electronic ignition system as they are much more reliable in the long run. another advantage is not having to remove the flywheel assembly to get to the points, which can become troublesome as you need a special tool to remove the starter mechinism (although i normally tap them lose with a hammer, but i would not recommend this). so try the obvious first then if you still have trouble ring a few mower shops and get a price on a secound hand electronic ignition coil (i wouldn't expect anything over $15 to $20). if they try to rip you off ill sell you one for $10 + postage (last time it was about $5)
so see how you go
regards jay