I doubt you would get the results you're looking for with a panel that small. Your deep discharge batteries will self discharge a little more than the multi purpose batteries do, it varies with age of batteries and storage conditions such as temperature. A 10 watt panel might keep up with this, barely, and only if the batteries are totally isolated from all parasitic type draws.
The above said, it sounds like you have a small parasitic draw but there is no way to say how big a draw it is without more information. Any way you can put an ammeter in the circuit to determine if there is a parasitic draw on your batteries or not?
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2016 Bighorn 3270RS, 2015 Ram 3500 CTD/ASIN
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