There are no hard and fast or statutory rules about procedures for co-option so councils need a a co-option policy which sets out how the process should be conducted. In the absence of an agreed policy guidance usually suggests that the process should be in an open meeting, including the voting. In my council, we invite candidates to give a brief introduction to why they want to be a councillor and then there's a vote. Our policy states that someone can ask or a ballot (paper vote) which does tend to happen but the basic procedure is a show of hands vote unless someone asks otherwise.