As an FYI, on the IP CYO series the light output seems to be quite constant, independent of speed, even at high speeds (>25 on our tandem, for example). But once you (which is to say, I or we) stop the light output takes a distinct drop, clearly bi-modal. This isn't the result of voltage dropping but must be a design feature. In any case, though available current does affect LED output it isn't the preferred way to modulate an LED. PWM is the standard way to do that, so a small micro-controller would seem obvious. At least that's how I read the riddle.

However it is true that as the super-cap runs down the LED gradually dims.