Yeah when I got mine I thought they had sent me an empty display box it was that light. I don?t have an alarm either and forgot to plug mine in when it came off the road for winter,plugged it in last week and was showing some discharge but nothing to be concerned about,and that was after 3 months on no use. If I remember right I had it plugged in all last winter to optimate lithium.
So to answer your question,either or appears to be the answer,just don?t let it go flat.
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