City Council may appoint by resolution at least one, but not more than three, residents of the City to serve as alternate members of the Board. The term of office of an alternate member shall be three years. When seated pursuant to the provisions of this section, an alternate shall be entitled to participate in all proceedings and discussions of the Board to the same extent as provided by law for Board members, including specifically the right to cast a vote as a voting member during the proceedings, and shall have all the powers and duties set forth in this chapter and as otherwise provided by law. Alternates shall hold no other office in the City. Any alternate may participate in any proceeding or discussion of the Board but shall not be entitled to vote as a member of the Board unless designated as a voting alternate member pursuant to § 600-405C hereof. On the resignation of a voting member of the Board, an alternate member shall automatically become a voting member, in order of his or her appointment, to the unexpired term of the member who resigned.