If a vacancy in the office of the director is filled by appointment, and the vacancy occurred on a date so that, under Section 1780 of the Government Code, there is required to be an election at the next general district election to fill the balance of the unexpired term, then, notwithstanding subdivision (d) of Section 1780 of the Government Code, the person elected shall serve for a full four-year term, if the terms of office of the directors would continue to be staggered at each subsequent general district election.