If there are wires leading under the flywheel from the coil, the engine has points. if not, it doesn't.
If there are points, remove flywheel using procedure as suggested, but take measures to protect the thread on the end of the crank.
If there are no points, then the coil (mounted outside the flywheel) is the only component in the system apart from the plug and cut-out switch(es).
Coils DO fail - quite regularly in fact - about 1 in 5 ignition problems on an electronic ignition engine is a coil falure. Points type coils are inherently more reliable, but the newest of them will now be 20+ years old, and moisture will have compromised most of them by now.
You can replace the points with an electronic module and retain the coil (if good), or you can replace the entire coil with an electronic version (cut the wire going to the points). Either of these is 'fit and forget'
Phil Saunders, March 2009