Biennially at the first meeting of the new council the members thereof shall choose a chair from among their number who shall have the title of mayor. In addition to the powers conferred upon him or her as mayor, he or she shall continue to have all the rights, privileges and immunities of a member of the council. If a vacancy occurs in the office of mayor, the members of the council at their next regular meeting shall select a mayor from among their number for the unexpired term.