Is there actually an identification with "an I" (implying something permanent, that is the same across moments) or just ideas of I/me/mine occurring again and again, the illusion of "me" getting created moment by moment?
There is no identification with a permanent "I" because there is no permanent "I", therefore it couldn't happen. However, there SEEMS to be a lifetime of conditioning that there is an I. The body/mind is most often thinking and acting in what it perceives to be the interest of that conditioned idea of "I" that it SEEMS to identify with.
Yes, ideas of I/me/mine are occurring (or are believed to be occurring) again and again. "I" am going to the store. This is coffee is "mine". These are "my" beliefs about that. It's not even spoken or thought about most of the time, things are just assumed to be identified with Pete or some other person/place/thing. That "I" am the individual doing/thinking/being various things.
Does the belief in I, actually identify with various thoughts? Can a thought think and identify? Or is identification just happening? Just process?
No, a thought cannot think. A thought IS thinking, it IS just a thought. That's very interesting. The belief in "I" is "made of" thoughts. The "I" thought wouldn't be able to identify with other various thoughts if a thought cannot think. There are certain thoughts that seem to be clustered together and be in harmony, they seem to identify with each other and create "me". When disharmonious thoughts or events occur, there's a sense of "get that away from me, that's not 'me'."
As far as I can tell, the sense of identification with a thought has no "power" to make anything happen on its own. The thought "you should go to work today" will probably be acted upon. The thought "you should go punch that guy in the face" will probably be ignored (thankfully). But both of them on their own have no ability to force anything to happen. There is just a sense of identification with this idea but not that one. The identification happens. The body acting or not happens.
Yes, identification is just happening. Or appears to be just happening anyway. There is a SENSE of identification. From one perspective, a SENSE of identification is necessary because without it the body/mind would die. If there was no sense of identification with anything in its own self interest, it couldn't survive.
You asked "Just process?" If that means that identification is just an activity, then I would say yes, it's just process. Identification feels like a verb, not a noun. Identification SEEMS to be something that's written in stone... these are my beliefs, this is how I want things to work. But in actuality, maybe it's just thoughts and actions occurring spontaneously. The world of the "I" thought has been reinforced for so many years, things just happen in alignment with those thoughts. The machine has been programmed a certain way, so to speak.
I keep thinking of cavemen and babies. How would a caveman or baby look at all this. Haha.
Continue looking: Is there anything that is identifying or does "identifying" (whatever exactly that is) just happening? What is actually there, seen in real time?
There are thoughts that arise sometimes that there is a lot of passion or anger or strong feelings around. A lot of ranting about a life situation has been happening today. There are strong sensations that occur in the body. There is an idea that occurs saying "I" identify with this because the sensations are so strong and the thoughts are so forceful. But identification is just another thought. And there is no I/me/self/Pete. So what is the body/mind getting so worked up about?
I say that this idea of what "I" am is a cluster of thoughts, beliefs, sensations, etc. but all of those things are just arising in the moment and fading away. There is no fixed thing "identifying." You could say identifying is just happening but it has no permanence or individual existence. There is nothing actually there, seen in real time.
Everything experienced in life seems to be a cluster of labels. A pencil has shape and color and purpose labels. "I" and "Identification" are collections of labels. When the labels aren't there there's nothing to say. Identification is meaningless. There is nothing seen in real time. This is not "my" phone, it's just an object. This is not "my" belief, it's just thoughts, and what's behind them I can't give a name to because to name it is to give it a seemingly independent reality.