Upon a vacancy occurring in the board by reason of death, change of residence or resignation or for any other reason, the governor shall appoint a qualified elector of the authority as successor to serve the unexpired term; provided that if the vacancy occurs after the single-member districts are created pursuant to Subsection B of Section 72-20-10 NMSA 1978, the qualified elector appointed shall reside within the district in which the vacancy exists.
NMS § 72-20-12