N.M. Stat. § 49-3-4
That within thirty days of the expiration of the terms of office of such board of trustees, it shall be the duty of such board of trustees to call an election for the choice of their successors; to fix the time and place for the holding of the same; to appoint qualified persons to act as judges thereof and to give notice of such election by posting not less than five notices in conspicuous places within the exterior limits of the said community lands of the said people of Chaperito for the length of time as specified in the preceding section [49-3-3 NMSA 1978]. That the terms of office of such members of such board of trustees shall be for the period of two years and the elections herein provided for shall be held on the first Monday in September of each alternate year, commencing with the first Monday in September, 1922; provided, however, that the trustees elected at the election called in accordance with Section 3 [49-3-3 NMSA 1978] shall hold office only until their successors are elected at the election to be held on the first day of September, 1922.
NMS § 49-3-4