If an officer named or referred to in sections 2.1015 to 2.1040 and duly authorized deputies are unavailable, the emergency interim successor highest in rank in order of succession who is available shall, except for the power and the duty to appoint emergency interim successors, exercise the powers and discharge the duties of the officer. The emergency interim successor shall exercise these powers and discharge these duties only until the time a lawful incumbent officer or duly authorized deputies or an emergency interim successor higher in rank in order of succession, exercises, or resumes the exercise of, the powers and discharge of the duties of the office, or until, where an actual vacancy exists, a successor is appointed to fill the vacancy or is elected and qualified as provided by law. The council, either by ordinance or resolution, may at any time terminate the authority of emergency interim successors to exercise the powers and duties of the office to which they have succeeded.