The council voted unanimously to raise the issue again at the next council meeting, to give staff time to answer questions from elected officials.
The council has been investigating the pathway for at least 15 years but has no up to date information about what it would cost and what it should look like.
The next phase of work, expected to cost up to $300,000 during the next year, would gather the information to answer those questions.
Coastal resident Eamon O'Connor, who spoke in the meeting on behalf of the Tauranga Harbour Protection Society to oppose the pathway, said Brownless should have used his casting vote to stop the project.
"Hopefully the council will see sense and work through this at the next meeting."
Chris Ingram of Bike Tauranga spoke in support of the project, saying it was an essential piece of infrastructure.
According to the council's latest round of community consultation, there is broad support for the pathway idea.
Of 1342 submissions, 1199 were in support and 127 were opposed. The rest were unclear.
The consultation was criticised by both councillors and a resident, however, for being weighted towards the benefits of the idea and lacking specifics about costs or design that might change people's perspectives.
Councillor John Robson said in the past, "when the community is confronted with the cost of something they say no".
The next phase of work would answer detailed questions about design and costs.
"We have been down the path too often of putting numbers on things that are wrong and I am reluctant to continue doing that.
"It is what we have done historically and invariably we get it completely wrong."
He said the next phase of work was an opportunity to reset the project and have an informed discussion.
Public spaces team leader Doug Spittle said it was not possible to put an accurate cost estimate on the project without a concept plan.
He said the pathway was likely to be 5m to 6m wide and about 900m in length, from Memorial Park to near the Harbourside Restaurant.
A high-level desktop estimate by Aecom put the costs of building a rock revetment of that size at $5.6m ($6250 a metre) and a boardwalk at $3.3m ($3700 a metre).
Spittle said the actual full project cost would likely be "significantly" higher as Aecom's estimate did not include contingency, legal costs and other estimates.
An estimate several years ago, when the council considered combining the path with the Southern Pipeline construction, put the pathway cost at $6m to $12m. That plan was eventually rejected.
