To test the magnets, see how well a screwdriver will stick to the magnet.
Check the plunger for the points to make sure it isn't sticking.
To rule out the coil, I would use an auto coil wired thru 12v and to points to see if it stays running. Not sure how available the magneto/coil under the flywheel is. If you switch to a regular coil, you have to add a power wire and use a mower coil.
A regular might post instructions on how to test he magnetto with an ohm meter.