Do you know what year your boat is? It is rare that a 1980-85 model would leak that much at the CB pivot as it is mostly external, with just 4 screws penetrating the hull, although they could still leak!
The 1971-79 models had a bolt through the CB trunk that held a plastic bushing in place inside the CB trunk and the CB pivoted on that bushing. These boats can leak around that bolt if it is loose or the rubber gaskets are worn out. With either vintage DS II the CB should be raised most of the way while moored (anchored or in a slip), yo ucould raise the Cb all the way, but if on a mooring or anchor, the boat seems to sail arounf less if the CB is down a little. Anyway, there is no difference in any "seal" whether the board is up or down, other than with it up at least most of the way it will reduce the side to side banging of the CB as the boat rocks. So, the below pictures/diagrams show first, the 1971-79 pivot setup, and the rest show various details of the 1980-85 version.
The way that the Day Sailer II deck and hull are molded fortunately creates a "boat within a boat" assuming there are no leaks i nthe deck/cockpit molding, that plus the built-in foam flotation limits how far a DS II will usually flood while moored. Still, it is very important to always open those Inspection/Bailing ports and remove any water that has collected since last use, before sailing! Hopefully, we rarely find much!