Voting will close on December 20 with the result announced later that day.
Only two candidates from the earlier farmer-director election, former director Leonie Guiney and former Zespri chairman Peter McBride were successful in getting more than 50 per support from voting shareholders.
Three other candidates, Nicholls, Tuuta and Waugh failed to make the required 50 per cent, leaving one seat on the board unfilled.
Farmers' dismay at Fonterra's performance was evident not only in their failure to re-elect board nominated Waugh but also in not supporting board-nominated Tuuta.
Guiney, who recently settled a defamation claim with the Fonterra board, was self-nominated with farmer backing, and McBride was board nominated.
The council's decision to limit the new contest to Nicholls and Tuuta instead of opening it to all newcomers reflects councillors' recognition that farmer-shareholders who backed Nicholls' self-nomination would react negatively if their voice was not acknowledged.
"New candidates will have the opportunity to put themselves forward in 2019 as part of the 2019 director election cycle," Coull said.
No third election would be held if neither Tuuta or Nicholls achieved more than 50 per cent support, he said.
If both got more than 50 per cent support, the highest vote achiever would be elected.
The board could make a temporary appointment until next year's annual meeting if the vacant seat was not filled.