In the local club there are 2 styles of rides that the organized rides fall under. Every listed ride has a leader (or 2).

One style of ride is indeed then led by that leader (if there are 2 of them, then the other acts as sweep). Periodically, the leader will let others take the lead for a period of time if they want to allow. These kinds of rides will then experience the longer pull leads you might be witnessing.

The other style ride is typically advertised, or due to its listed level (eg. A and/or B) as being a rotating paceline ride. Typically about a minute, sometimes adjusting longer if there's a hazardous/narrow patch of road that's not favorable for 2-abreast space.

Either way, ideally whoever is the registered "leader" of the ride, should be setting the 'rules' and communicating them to the group before the start.