Disaster successors may act in the office to which appointed only:
A. in case of a disaster declared by the chief executive officer of the United States, and the chief executive officer of the state, and as long as a state of martial law is declared to exist or until a duly elected or appointed legislature, fulfilling all constitutional requirements, declares by joint resolution that the disaster emergency period has ended; and
B. the officer or authorized deputy in whose stead they are acting is unavailable; and
C. any disaster successors who are ahead of them in the line of succession to the office are unavailable; and
D. a successor to the office has not been selected and qualified as provided by law, other than the Disaster Succession Act [ 12-11-1 to 12-11-10 NMSA 1978].