The mayor shall preside at meetings of the council, and be the recognized head of the city for all ceremonial purposes and by the governor for purposes of military law. The mayor continues to have all the rights and privileges as a member of the council. If a vacancy occurs in the office of mayor or if the incumbent is absent or disabled, a mayor pro tempore shall be selected by the council from among their number to act for the unexpired term or during continuance of the absence or disability.