She said the delay with her formal resignation was "purely to save the taxpayer money" and it would be signed and sealed as soon as Mr Cozens acted.
Resignations take effect as soon as they are presented in writing and formally accepted, requiring local authorities to immediately start the process of replacing the vacant member's seat.
A third party, former Turangi-Tongariro ward councillor and long-serving community board member Maggie Stewart was waiting to see if Mr Cozens is going to act on his threat of resignation.
Mrs Stewart, who narrowly lost her council seat at the last election, said she would be interested in standing in the by-election.
"I have unfinished business with Turangi," she said.
A Turangi-Tongariro by-election process has begun and it is expected to be held in early October.