When any vacancy shall happen in the office of mayor by death, resignation, absence from the city, removal from office, refusal to qualify, or otherwise, the president of the council for the time being shall exercise the duties of the office of mayor, with all the rights, privileges and jurisdiction of the mayor, until such vacancy is filled or such disability is removed, or, in case of temporary absence, until the mayor shall return; and in case of such vacancy, other than temporary absence or disability, the president of the council shall become mayor. Thereupon the council shall elect from its membership a new president of the council. Whenever a vacancy shall occur in the office of councilman, the governing body shall appoint an elector of the ward where the vacancy occurs to be councilman for the balance of the unexpired term.