Yeah, the operation of this light is something that really bugs me.
What's the point of an indicator that doesn't change state when the switch is toggled?!?!?
I've got a brilliant idea - howsabout a light that's one color when the battery is in "use" and another when it's in "store"? Or a light that's on or off under the same conditions? Or superdeluxe: one state when battery's in use and the converter isn't powered, another when the battery is in use and the converter is powered, and a third when the battery is in store and the converter is powered.
It's not like we haven't had dual and even tri-colored LED packages for the last 30 years, and it's not some major engineering problem to design the appropriate circuit. Nor should the parts come to more than a coupla bucks.
Hmm, sounds like another little project I don't have time for....