The Board of Selectmen shall appoint for a term of two years a Town Meeting Moderator and a Deputy Town Meeting Moderator who shall have the powers and duties prescribed by law. Said appointees shall not be of the same political party. The Town Moderator and Deputy Town Moderator shall, at the time of their appointment, be a resident elector of the Town of East Lyme and in the event they cease to be a town elector, they shall cease to hold the office and the office shall be deemed vacant.