The Board, upon petition by at least 10 percent of the producers in the Commonwealth as determined by the Commissioner, shall provide for a referendum on the continuation of the Apple Board or amending the excise tax on apples if established pursuant to § 3.2-1208. The Board shall not act on such a petition for conducting a referendum until at least five years have passed since the last referendum. Any referendum held under this section shall be conducted in accordance with this chapter.