N.M. Stat. § 49-2-4
The election provided for in the preceding section [49-2-3 NMSA 1978] shall be held by three judges who shall be owners and proprietors residing upon said grant, and the heads of families, and shall be designated by votes of two-thirds of the trustees present at the regular meeting of such board of trustees held in October next preceding the date of such election. No more than two of such judges shall reside in the same precinct, if there be more than one precinct in such land grant. It shall be the duty of the outgoing board of trustees to give notice of the time and place of such election by posting not less than three notices in public places in each precinct in which the grant is situated, such notices to be in both the English and Spanish languages, and to be posted not less than twenty days before the date of such election. Said elections shall be by ballot, and each ballot cast shall have the name of the voter casting the same written thereon, and all ballots shall be preserved by the judges of election until the next ensuing meeting of the board of trustees, and so much longer thereafter as said board shall direct. It shall be the duty of such judges of election to canvass the ballots cast at such election and issue certificates of election to each of the nine persons receiving the highest number of votes cast at such election, and such certificates will authorize the persons to whom they are respectively issued to discharge the duties of such trustees for the term for which they were elected and until the election and qualification of their successors.
NMS § 49-2-4