The election of trustees of a rural improvement zone shall take place at a special election on ballots which shall not reflect a nominee’s political affiliation. Nomination shall be made by petition in accordance with chapter 45. The petition form shall be furnished by the county commissioner of elections, signed by eligible electors of the rural improvement zone equal in number to one percent of the vote cast within the zone for governor in the last previous general election, and shall be filed with the county commissioner of elections. A plurality shall be sufficient to elect the five trustees of the rural improvement zone, and no primary election for that office shall be held. At the original election, two trustees shall be elected for one year, two for two years, and one for three years. The terms of the succeeding trustees are for three years. The terms of the trustees shall begin immediately after their election and certification. The trustees must be residents of the zone. Vacancies on the board shall be filled by appointment by the remaining trustees.