It seems to me that the best alternative to dimming (and maybe an even better outcome than dimming alone) would be to
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Illuminate the green lamp indicating that the battery is charged [or charging] and working correctly ONLY when the keypad is illuminated. So it would only illuminate when the keypad is being operated.
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Illuminate warnings at all other times that the battery indicator would otherwise be illuminated. So, even if the keypad was not being used, it would display battery warnings.
For me personally, it seems that would be ideal.