Weak spark - 8HP Tecumseh
Okay, for whatever reason, I had a picture of a 5 HP B&S or something like that in my mind. You're right; my 70'ish rototiller has that engine, and the mag is behind the flywheel, but I have only had it off maybe once or twice to blow the dust out, and can't recall exactly what it looks like. If it were me, I believe that I would still proceed along that path, remove the flywheel, clean the inside surface, and see what you can see. Check that the key is in good shape, probably replace it as long as you're in there, that the coil hasn't loosened and backed away from the flywheel, and that the condenser is tight, and not grounding itself out. Otherwise, since it sounds like the condenser and points are not too old, I would probably break down and try to find a coil. Backing up though, I don't know what that has for a kill button and interlocks, but it would be well worth chasing that circuit with an ohmmeter first, just to make sure it's not grounding itself out.