Reelight SL-120 circuit theory and making it flash flasher

I noticed the other day that my front, white, Reelight SL-120 had a crack in the plastic. Since it was partially cracked and needed to be fixed I decided to take it apart to see how it operated.

Reelights work through magnetic inductance. Two magnets on the spokes of the wheel spin around and briefly pass by the light. The light has an iron core that meets the magnets as they pass by. The iron core is wrapped with enamel coated wire. As the magnets pass by the iron core, the collapsing magnetic field creates and electric current that travels through the wire. The electric current in the wire travels

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