An office shall be deemed vacant upon the incumbent’s death; adjudicated incompetence; conviction of a felony, other offenses pertaining to that office, or unlawful destruction of public records; resignation; recall from office; or ceasing to possess the qualifications for the office; upon the failure of the person elected or appointed to the office to qualify therefor within ten days after the time for the term of office to commence; or in the case of a mayor or councilors, upon the mayor’s or councilor’s absence from the city for 30 days without the consent of the council or upon the mayor's or councilor's absence from meetings of the council for 60 days without like consent, and upon a declaration by the council of the vacancy.