(a) If a vacancy occurs in any elective office or in the office of Assessor, Attorney, Clerk, or Treasurer, the Council shall, within thirty days after such vacancy occurs, appoint a person who possesses the qualifications required of holders of the office in which the vacancy exists to fill such vacancy for the balance of the term of the person whose office is so filled. A vacancy in the office of City Manager shall be filled within ninety days.
(b) If a vacancy occurs in any appointive office, other than that of City Manager, Attorney, Assessor, Clerk, or Treasurer, the Council shall, within thirty days thereafter, appoint a qualified person to fill such vacancy in the manner required for making the original appointment.