The mayor of any city having fewer than twenty-five thousand inhabitants as determined by the most recent federal decennial census or the most recent revised certified count by the United States Bureau of the Census, by and with the consent of the council or a majority thereof, and the chairperson of the board of trustees of any village, by and with the consent of the village board or a majority thereof, may appoint a board of not fewer than three nor more than six members, to be known as the cemetery board, from among the citizens at large of such city, or from among the citizens at large from the county or counties in which the village is located for such village, who shall serve without pay and shall have entire control and management of any cemetery belonging to such city or village. Neither the mayor nor any member of the council nor the chairperson nor any member of the village board of trustees may be a member of the cemetery board. At the time of establishing such cemetery board, approximately one-third of the members shall be appointed for a term of one year, one-third for a term of two years, and one-third for a term of three years, and thereafter members shall be appointed for terms of three years. Vacancies in the membership of the board other than through the expiration of a term shall be filled for the unexpired portion of the term.