Do you have a model number for the engine?
are they actaully magneto or CDI on that engine? The only info I could find on a Honda 11hp vertical engine says it has Transistorized magneto igniton.
Usually a magneto engine doesn't have points, since the timing is controlled directly by the magneto location.
Engines with an alternator, use points and a coil, and usually have a battery to energize the coil. My 10 Hp Kohler has this setup. Some engines will run with out a battery but some won't, depending on the type of alternator.