The first alternate member, so appointed, shall serve for a term expiring three years from the end of the official year in which he is appointed, and his successors shall serve for a term of three years from and after the expiration of the terms of their predecessors in office. The second alternate member, so appointed, shall serve for a term expiring two years from the end of the official year in which he is appointed, and his successors shall serve for a term of three years from and after the expiration of the terms of their predecessors in office. Should a vacancy occur for reason other than the natural expiration of a term, the Town Board may fill the vacancy for the unexpired term.