That's odd... I have no idea what the difference would be between "select" and "appoint". I don't remember seeing that before. I think that "select" is a bug. It's probably not supposed to show up. I tried it on the dev server. You can select it, and it remembers the selection. But on the Realm Government page, the "selection method" is blank. It appears to function the same as "appoint".
But no, there is no selection method that would let you appoint and dismiss council level positions at will.
