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Multiple sources have confirmed the question came during the non-public section of a committee meeting early last week.
The mayor has previously said he had no intention of hanging up the mayoral chains prematurely, despite criticism mounting in the past year over his ability to lead.
Sir Tim's ninth term as mayor of Invercargill has been marked by the resignation of his deputy Toni Biddle, a damning independent review in November last year, a driver licence suspension in May, and ongoing discord with his councillors and staff.
"You get all these Covid-19 reports that anyone over 70 is virtually a gonner. And it does undermine your confidence a bit. You think, hang on, am I next?" he said last month.
"I don’t want to make any predictions, but all I can say is it’s my intention to run, at this stage."
It is understood the mayor’s question came against the flow of conversation during a June 21 risk and assurance committee meeting, triggering a response about the procedure of a by-election.
The items on the agenda for the closed part of the meeting included Sir Tim’s legal proceedings against his own council to recover his costs following a defamation trial.
The council’s progress addressing concerns raised in the independent Thomson Report, which was critical of Sir Tim’s performance, was also up for discussion.
Sir Tim could not be reached for comment, despite multiple attempts.
Invercargill City Council chief executive Clare Hadley would not respond to questions about what happened at the meeting.
However, she said two options were available to council in the event of a mayor resigning prematurely, depending on the timing of the resignation.
If a mayor resigned within a year of the next election, council could appoint an acting mayor in their place.
If the resignation occurred outside of that window, a by-election must be held.
"The choice of acting mayor is actually a choice for council."
The next round of local body elections is set for October 8, 2022, about 15 months away.
- By Matthew Rosenberg, Local Democracy Reporting