The Board, upon petition by members of the horse industry representing at least 10 percent of the number of members of the horse industry who voted in the preceding referendum, or as determined by the Commissioner, may provide for a referendum on the continuation of the equine infectious anemia test assessment in accordance with the provisions of §§ 3.2-112 and 3.2-1705. The Board shall not act on such a petition for conducting such a referendum until at least five years have passed since the last referendum. If the Governor determines that a simple majority is not in favor of the assessment, the Board shall hold no new referendum for at least one year after the Governor has declared his findings. The cost of conducting any such referendum under this section shall be from the Virginia Horse Industry Promotion and Development Fund.