Politics department lecturer Dr David Jenkins said he was going to present a motion in the public forum asking the university to "divest from corporations that are complicit in Israel’s violations of Palestinian human rights and breaches of international humanitarian law" and end "any existing contracts with these companies and pledge not to enter into new agreements with them".
However, before he could speak to the motion, the council decided to shelve it until a report by the university's senate on "institutional neutrality" was completed.
It then moved into public excluded.
A university spokeswoman said the motion was passed on to the council by the staff-elected representative on council, but there was no request for staff members to speak to the motion.
Dr David Jenkins said the situation left him confused about what went on.
"I don’t know if there were crossed wires, but it felt like they were trying to humiliate us in some respect.
"They made us sit through all their turgid administrative procedures, none of which we had any interest in; quite the contrary, in fact.
"We were asked to leave as soon as anything emerged with which we did have an interest, so it was a very strange experience."
Dr Jenkins said he and others had worked on a similar motion for the university senate, which had the support of more than 300 academic staff.
Initially, the motion also called for an "academic boycott" of Israel, but this proved contentious even with the academics who supported divestment of assets related to Israel.
"The frustrating thing is we don’t even feel like we’re at the door that we need to be knocking at.
"There’s no guidance on how to put these sorts of motions forward. You have to find out everything yourself."
Media studies and communications lecturer Dr Olivier Jutel, who also assisted with the motion, said part of the issue was the fact the university did not seem to want to investigate whether it had any investments associated with Israel.
"They have a stance that they don’t to ‘the best of their knowledge’, but they also don’t seem to want to investigate it."
A spokeswoman for the university said the council noted a similar motion had been put to the university senate which had agreed to pause consideration of that motion until the report of the working group on institutional neutrality had been completed and considered by the senate.
"The council agreed to await the working group’s report before considering the motion.
"The working group is progressing well and expects to present a report to both the senate and council early next year."
Dr Jenkins said the idea of institutional neutrality did not sit well with him.
"The university council constantly falls back on this argument of institutional neutrality, which I guarantee you no-one had heard of before this issue was raised, because no-one threw it up when it was decided that the university was a Treaty-led institution.
"It didn’t stop people coming out and condemning the Russian invasion of Ukraine."
An August letter from vice-chancellor Grant Robertson in response to an open letter from academics said "it is impossible not to be moved by what is happening in Gaza".
"As has been stated publicly on a number of occasions, to the best of our knowledge the university does not have any financial links with Israel.
"Many of us hold strong personal views on what is happening in Gaza. It is vital that as a university we provide an environment in which they can be expressed and respected.
"As an institution, moving beyond a position of neutrality may compromise the provision of this environment."
In October, Mr Robertson said a pro-Palestine protest "crossed a line" from being a peaceful protest when some of the protesters entered the clocktower building.
