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So I hooked up the meter and left it for a while. It settled out to .5 amp after about a minute and then steped down a bit every minute or so until after about 20 minutes it settled out to .011 amps draw.
Interestly, at about 30 minutes or so, it jumped up to .35 amp draw for about a minute, then dropped right back to .011 amp. Something must "wake up" every now and then.