Never mind the D and R honorifics for now. Most politicking never shows up in the news--it consists in jockeying for empires within and between bureaucracies.
Even in the armed forces, when fighting a common enemy, infighting and empire-building go on, and have been known to even involve assassinations. Not just the Japanese: we also lost some people in WWII because of inter-service rivalry (and politician stupidity).
So suppose the FBI and CIA are having a spat, or the NSA and the Pentagon, or NASA and the DOE. Or suppose there's an internal squabble in State. What might you expect to see?
Leaks, for one. Stuff that's supposed to be secret that somehow shows up. It might be embarrassing, or it might be supposed to be top secret and the agency responsible for the secret gets egg on its face for not keeping secrets. Or it might kill an ongoing operation that was Not Invented Here.
Embarrassing incidents, like the infamous "Reset" button. That whole idea was so tone-deaf that it had to be an enthusiasm from higher-ups, but the mis-translation on top of everything else really put the icing on the cake. Unless Hillary used the dictionary herself, somebody probably got fired for that little bit of carelessness--and if so, I'll bet it was the wrong person.
Strings of replacements of leadership. If one category of administrator or general officer seems to be systematically replaced by another, probably somebody lost the political struggle big time. One big problem is that you won't understand what you see, because outsiders don't always know what the categories are.
Noisy leaders or wannabe's or whistle-blowers that suddenly decide to retire to be with their families.
Agencies starting to arm up. Just in case, of course. Not for shooting, but so that the Department of Education doesn't let the Bureau of Land Management intimidate them when they show up in force at some contested site.
All these things happen all the time at some level, of course. How do you know when the activity is significant? When does it strike you that (e.g.) there've been a lot of high profile suicides lately? Is that random chance, greater popularity, more reporting, or more intense pressure? Note that a national database of phone contacts can with difficulty find a few terrorist needles in the haystack, but it is ideal for tracking the contacts of somebody you want to get the dirt on.
No, I'm not looking for conspiracies. You don't have to. This just seems like the kind of behavior you expect from competing bureaucracies. It might even be more bitter at the University level ("the stakes are lower"), but when the organizations get really big the troubles for the rest of us get bigger too.