Eventually a poll was taken on whether there should be a “head-to-head” vote, but this was narrowly defeated with Reform and the Conservatives voting against.
The meeting continued with councillors working through the rest of the agenda, deciding on other topics such as the formation of committees.
There was more confusion when councillors were called to decide on whether voting within the council would be proportional.
Though traditionally no councillors vote against, 27 voted “no”, including the newly elected Deputy Mayor Lee Cliff.
This led to further exchanges over which procedures were and were not understood by councillors.
The vote was then re-taken, and all members voted “yes”.
Eventually, still without a leader, the session concluded, with Reform UK immediately leaving for a group meeting.
The election of a council leader was postponed until next Thursday.
Reform UK is the largest party at Kirklees Council following the 7 May elections, with 29 out of the 69 seats, but falls short of a majority.
The Greens have 12, Independents 11, Conservatives nine, Liberal Democrats five and Valley Independent Group three.
The BBC has approached the Reform group for comment.
Additional reporting by the Local Democracy Reporting Service.