(a) The governing body shall, by two-thirds concurring vote, declare the office of mayor vacant only when the person elected

(1) fails to qualify or take office within 30 days after election or appointment;

(2) unless excused by the governing body, is physically absent for 90 consecutive days;

(3) resigns and the resignation is accepted;

(4) is physically or mentally unable to perform the duties of office;

(5) is convicted of a felony or of an offense involving a violation of the oath of office;

(6) is convicted of a felony or misdemeanor described in AS 15.56;

(7) is convicted of a violation of AS 15.13;

(8) no longer physically resides in the municipality; or

(9) if a member of the governing body in a second class city, misses three consecutive regular meetings and is not excused.

(b) A vacancy in the office of mayor occurring six months before a regular election shall be filled by the governing body. The person appointed serves until the next regular election when a successor is elected to serve the balance of the term. If a member of the governing body is appointed mayor, the member shall resign the seat on the governing body. If a vacancy occurs more than six months before a regular election, the governing body shall call a special election to fill the unexpired term.

(c) Notwithstanding (b) of this section, a vacancy in the office of mayor of a second class city shall be filled by and from the council. A mayor appointed under this subsection serves the balance of the term to which appointed, except the mayor may serve only while a member of the council.