Good question. For one thing, additional lighting, some required by law, has added extra load to the feeble electrical systems on these bikes. My 1963(?) Peugeot had no brake light and an AC horn that ran off the lighting coil and extinguished the headlight when you tried to sound it. So you had to turn off the headlight to honk the horn.
My Trac Clipper is a 1984, but if there's a horn diode in there I can't find it. It ran right off the ignition coil like yours, and stopped the engine, like yours. The diode might have been removed at some point. I'll stick an ammeter on the horn (do I have an AC ammeter somewhere?) to find the current.
The deal with current, voltage and magnetism is as follows:
(1) when electric current flows through a wire, the wire becomes magnetic. This effect is magnified many times when the wire is very long and wound into a coil with many turns. We get even more magnetism if that coil is wound around a piece of iron or steel. This device is known as an 'electromagnet.'
(2) Conversely, if we have a coil like that described above, we might bring something magnetized close to it. We could say that it then has magnetism--we call it a 'magnetic field'--running through it. Now, if we happened to change the amount of magnetism flowing near that coil--say, we pushed the magnet closer or took it away or flipped it over--then we'd see a voltage, or electrical pressure, generated at the ends of that coil's wire. A large, fast change in magnetism near the coil will produce a large voltage across the ends of its wire. Then, if there's a path for it to take, a current will flow from one end of the coil wire to the other. This is an electric generator.
So: an electric current flow will produce magnetism in a coil, and a change in magnetism near a coil will produce a voltage and, if the path for it is complete, a current.
Now connect an electric generator consisting of our flywheel magneto coil to an electromagnet, which is one of the two separate coils (the 'primary') inside our spark coil assembly. The magnet on the flywheel rapidly approaches the magneto coil, which rapidly changes the amount of magnetism through that coil. This generates a large current through both both the magneto coil and the primary coil. Hence we get a lot of magnetism through the primary coil _and_ through the secondary coil.
When the points open, the amount of magnetism through all coils drops from a lot down to zero in a very short time. This rapid change in magnetism creates a very large voltage across the ends of the secondary coil, and this is applied to the spark plug.
Only the abrupt change in magnetism caused by the opening of the points can generate enough voltage in the secondary of the spark coil to arc the spark plug gap.