Subject to subsection (b) of this section, a holder of a Class E water vessel license operating on State waters in the county may sell beer, wine, and liquor on Monday through Saturday, from 6 a.m. to 2 a.m. the following day. The Board shall determine when the license holder shall stop selling alcoholic beverages on December 31 and the morning of January 1, regardless of the days of the week on which these dates fall.