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Cr Vandervis allegedly shouted at deputy mayor Christine Garey and pointed his finger in her face after a council meeting on July 28.
Independent investigator Steph Dyhrberg found Cr Vandervis breached the council's code of conduct.
Councillors unanimously backed a motion put forward by Cr Chris Staynes suggesting councillors accept the findings of the report and require Cr Vandervis to provide an "unreserved, written and public apology for his aggressive and intimidating behaviour".
If no acceptable apology was received, the council would revoke Cr Vandervis' membership of the Otago Museum Trust Board and District Licensing Committee.
Cr Staynes and Cr David Benson-Pope suggested Cr Vandervis could benefit from seeking professional help or taking an anger-management course.
Cr Benson-Pope likened Cr Vandervis' conduct with that of a rugby player screaming at a referee.
He said Cr Vandervis continued to be in denial and Cr Benson-Pope urged him to take responsibility for his behaviour.
Mayor Aaron Hawkins compared Cr Vandervis' reaction with that of his four-year-old son, who was sometimes agrieved when called out for his conduct.
Mr Hawkins said the behaviour of the councillor was embarrassing.
Cr Sophie Barker said professional, courteous behaviour was needed in the workplace.
"It is completely unacceptable to bail someone up and shout at them."
The debate over Cr Vandervis' actions got under way at 1.30pm and began with him defending himself. He disputed the appointment of Ms Dyhrberg as investigator, he said, reading from a statement he sent to the Otago Daily Times just ahead of the discussion.
"This code of conduct report has been written by an investigator whose previous DCC code of conduct report was so deficient that she omitted to interview or communicate in any way with the complainant, completely contradicted herself on the fundamental issue of materiality, and ignored written first-person email evidence."
He disputed accusations he was "screaming and yelling" and that his face was only 20cm from Cr Garey.
However, he withdrew a comment about Cr Garey's make-up after reading the following from his statement:
"Deputy Garey and Cr [Steve] Walker have accused me in this code of conduct of being excessively tall, male and red in the face. As Cr O’Malley noted, I have a ruddy complexion anyway.
"Regarding the other accusations, I refuse to have height-corrective or transgender surgery, or to employ make-up like Deputy Garey to hide my true face."
Cr Garey issued a statement afterwards thanking her colleagues "for their definitive and emphatic response with the tools they currently have available to them".
"The wider issue is that there are limited tools within local government to deal with such extreme behaviour," Cr Garey said.
"I welcome the work that has already begun at a national level to address this matter. I will continue to support these efforts to ensure that we have the means to hold people to account within local government."
Cr Staynes said he expected that in the private sector, such offending would at least result in a formal written warning and, for multiple breaches, in dismissal.
Cr Vandervis previously issued an apology for "loudness", though other councillors have called the apology weak and pathetic.
Cr Garey and two other councillors, Steve Walker and Marie Laufiso, laid complaints the day after the July meeting.
Mr Hawkins and seven councillors deliberated.