Local Government New Zealand chief executive Malcolm Alexander said the law was clear.
"Each mayor has the power to appoint a deputy and each council has the right to take issue with that and appoint another one should they wish.
"The only way the current deputy mayor [Bishop] can be overturned, is by vote of council.
"Of course it's open to any citizen to take issue with legal interpretation and that's why we have courts."
Alexander said Feyen's announcement did not alter the legal position of who was the deputy.
"There is a council that is operative and is making decisions, it's business as usual."
Feyen said as far as he was concerned, the deputy mayor was Campbell because he did not trust Bishop.
"Ross [Campbell] has been essentially the deputy mayor, even though he hasn't been getting paid, because he is the one who has been there.
"He has been a massive help."
Feyen said he believed he was fighting for democracy by questioning section 41A of the Local Government Act.
Acting chief executive Monique Davidson echoed Local Government New Zealand's stance and said Bishop was deputy mayor.
She said the council was getting on with business as usual.
"We have a role to do and that is to deliver on our contract with our community."
Next week the council will meet again to begin hearings on its annual plan.
"I have every confidence that through free and frank advice from officers, and transparent and robust debate form elected members ... that elected members are able to make quality decisions," Davidson said.
Councillor Christine Mitchell said it was becoming harder to "get on with it" and dealing with personality clashes was a waste of energy and time.
"We just have to plod on."
"I just hope in time the mayor realises there are other people elected to the council and it's a democracy."
Councillor Bernie Wanden said it was not a good look for the district having the council constantly discussing personality issues.
He said if it continued, it could deter people from running for council in the future.
"We're at a crossroads in terms of how we go forward from here.
"It could be really interesting because unless the mayor is prepared to put forward ideas and issues that we can all debate and talk about and then vote on, then I am a little concerned about our future."
Wanden said councilors were being tainted by the mayor's "shenanigans".
"It's not productive that they're not allowed to get on with the job that they're elected to do."
Councillor Ross Brannigan said elected members wanted to deal with local issues and personality clashes were a hindrance to that.
"If it was that easy, I think you'd find a number of people would walk but we have a responsibility to the people who elected us."