Tecumseh charging coils output "half wave AC" which means one AC leg is "grounded" to the engine block, and the other leg connects to a wire. It will power an electrical load connected across the legs (engine block and wire).
Dual half wave outputs are common. Each leg can power a load. For example, one leg powers a headlight bulb with AC, and the other leg powers a diode rectifier. The rectifier converts AC to DC, for battery charging.
You are right, LED's are diodes... and they run on DC power. You can power LED's from the Tecumseh rectifier. At idle, the LED may pulse on/off as the magnets on the flywheel turn slow. Flickering and on/off ops can be corrected with a capacitor.
You can run dual diodes (Tecumseh did it) into a single DC "bus" that sums the Amps from both outputs. This is enough power to charge a battery and run LED's. Battery = bright at all speeds. With no battery, a capacitor will smooth it.
I have 6 Amp diodes on hand that will work. Glad to send a few if you want to run those. This diagram I drew shows the double diodes/DC bus setup powering incandescent bulbs. Easy to replace with LED's.
Jon Pardue