Except in the case where a county board of supervisors has appointed itself as the district board, each member of a district board and each member of a fire commission appointed pursuant to Section 13844 shall be a resident of the district. In addition, if the district board is elected, each member of the district board shall be a registered voter of the district. In the case of a district board which is elected by divisions, each director shall be a registered voter of the division from which he or she is elected.