Turning the Battery off

Reading back above, I see two (or more) Dorado battery charge light behaviors: one kind in which the lights turn on and off with a long press of the button, staying on while the bike is On or charging, and one in which the lights ONLY come on with a button press (not while the bike is On or charging) and go back off as soon as the button is released. I now have one battery displaying each behavior. I'm ok with this, but just tonight I noticed that the pack with the 'press only' behavior also does not auto shut off. Should I be worried about this pack, which I just bought from Ebay...?
 
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