Any vacancy on the board shall be filled by appointment by a majority of the remaining members of the board. The appointee shall serve until the next local election pursuant to the Local Election Act [Chapter 1, Article 22 NMSA 1978] when the vacancy shall be filled by election. If the board fails to fill any vacancy within thirty days after it occurs, the court declaring the organization of the district shall fill the vacancy.
NMS § 72-18-15