A vacancy shall be filled by appointment for the unexpired term, except as provided in AS 39.05.080 (4), and all vacancies shall be filled within 60 days. Except as provided in AS 39.05.080 (4), after the expiration of a member's term of office a member continues to serve until a successor is appointed and qualifies, formally advises the board of acceptance of the appointment, and appears at the next meeting of the board.