Completely OT question (electrical engineering)

On Saturday, May 16th, I purchased a brand new shiny (really, it's shiny! silver!) moped.

Yay.

No, it doesn't have any electrical problems. Or mechanical problems. It has "Lumi has never ridden a powered two-wheeled vehicle before" problems, but those are irrelevant to this.

But what it also doesn't have is a battery. The electrical system on this moped is driven by the engine. Turn it off, no juice. Turn it on, juice. A magneto to generate electricity when the engine is turning over and a regulator to keep the electricity within a specified range of volts and watts. Very simple, just enough to power a headlight, brake light and turn signals.

The "issue" I'm having is a direct result of the way this system works. With the electrical system being dependent on engine revolutions, the slower the engine goes, the less power there is for the lights, so the headlight dims and flickers when I slow down or stop.

I know I can't make it stop going dim without installing a battery, so I'm not really concerned with that. What I want to do is stop the flickering. So what I was thinking was, wouldn't I be able to stop it from flickering by wiring a capacitor in behind the headlight connector? Now, I don't have a degree in electrical engineering, or even do much of anything with electrical components (hands shake too much to hold a soldering iron steady), but I understand what capacitors are, and how (and why) they work, and from what little I do know, this seems like a viable solution.

With a capacitor, what I would expect to happen is, the capacitor charges up on the incoming electricity, and acts as a buffer, so even when the power in the system itself is coming in bursts, the capacitor should release a steady stream of electricity to the headlight as long as it holds a charge. And that should, if I'm right, be just enough to alleviate the flicker.

Yes? No? Banana?

The headlight is 12v 25w/25w. The magneto generates 12v 80w (peak?), and there's a 12v 60w AC (yes, AC, not DC) regulator. I've read dozens of reports of people running 12v 35w/35w headlights on this electrical system (if that information is useful in any way). So what, in "Lumi is a stupid doodyhead who don't know nothin'" terms, type of capacitor would work best for this, if it will work at all?

I might be completely wrong, but it is my understanding that capacitors are moreso for preventing current surges rather than maintaining a steady current. If that is true, I think a voltage regulator is what is required.