Many thanks for the suggestions.
Les, looking over the link you furnished I don't think I want to go that route. Andrew, that's an interesting idea, however; the meter "seems" to turn off, that is the LEDs don't show. If current is still sent to the meter cell that might explain the drain. I wonder if a bit of vinyl adhesive tape to the inside of the bottom cover where the switch might contact it would be worth a try. Hmmm, it'd be only yet another couple of cells shot....