kremlinology is an old pre-1989 term for people trying to observe and interpret the workings of a tightly sealed institution. Could be used for Vatican rumors and news, too, for example, or North Korea, etc.
Stuff like watching the order of names on public lists of attendees for dinner events, etc. If someone disappeared or moved off the top few names, perhaps they're in trouble or have been purged from the party ... or maybe they're just sick this week.