(A) A vacancy in the Council shall be filled by a majority vote of the remaining members of the Council. If the vacancy occurs subsequent to twenty days before the date when candidates for the office of Council member must file their nominating petitions or if two years or less remain in the term of the incumbent who created the vacancy, the person elected by the Council shall serve for the unexpired term. If the vacancy occurs at least twenty days prior to the date when candidates for the office of Council member must file their nominating petitions and more than two years remain in the term of the incumbent who created the vacancy, the person elected by the Council shall serve until a successor is elected at the next regular municipal election and qualified to serve for the remainder of the unexpired term. The person elected for the unexpired term at the next regular municipal election shall take office on the first day of January following his or her election.
(B) If the Council shall fail to elect a person to fill a vacancy in the Council under Division (A) of this Section within forty-five (45) days after the occurrence of the vacancy, its power to do so shall lapse and the Mayor shall appoint a person to serve for the time as provided in Division (A) of this Section.