Any person wishing to become a candidate for the office of director in any district shall file a declaration of candidacy pursuant to the provisions of the Local Election Act [N.M. Stat. Ann. Chapter 1, Article 22], stating the election precinct for which the person is a candidate, accompanied by a petition signed by not less than ten qualified electors of the election precinct for which the person is a candidate to represent. No declaration of candidacy shall be accepted unless accompanied by such petition, signed by electors.