Any grower may place his or her name on a candidacy list for appointment as a grower member of the commission by filing a petition signed by at least ten resident bean growers (1) from the district in which he or she resides for an appointment under subsection (1) of section 2-3746 or (2) from the district in which he or she resides or the other district to be represented for an appointment under subsection (2) of section 2-3746. The petition shall be filed with the commission. The Governor and the commission shall make appointments from the candidacy list unless there are no names on the list.