Most gliders are privately owned, and most of those are in what you call equity groups (usually termed glider syndicates in our world). A smaller number, but growing, are single ownership.
Non-equity shares are unusual, but not entirely unknown. They typically arise when a glider is doing less flying that it could and its owner allows one or two friends to share by paying a share only of annual running costs. I never heard of anyone setting up such an arrangement as a way of starting a syndicate. Don’t rely upon finding one if you plan to take up gliding. Clubs are in effect large non-equity groups, and that is the route for people who can afford the costs on a day to day basis but not a capital investment. Almost all clubs have one or more single seat gliders for this purpose.
A flying programme as you ask does not exist. For people wanting to fly club gliders, there is usually a daily list – first come first served. A few clubs have a booking system. I never heard of any club allocating tow capacity between private and club gliders. It just doesn’t work that way. There have been times when so many people want launches that a period of priority is given to club gliders by pushing them to the front of the queue when they land, and other times when a cross country group, especially a competition start, is given priority. Otherwise, most places launch in the order gliders arrive at the launch point.
HTH. ChrisN.