@Jon, it completely makes sense and is an excellent and helpful articulation of how immersion works for you. All I’m saying is that, as you note, it works differently for different players, and also that the taxonomy of stances sometimes fails at describing actual play experience. For some people, the jumping back and forth does not exist — it may be a more fluid shifting, or a kind of immersion that encompasses multiple stances at once.
As an aside, I am confused by one aspect of your example:
Now you ask me to paint the scene. “It’s a dingy faux-Irish pub that’s seen better days. What do you see that tells you it’s a hive of scum and villainy?” Are you asking Anna or Jon?
If I am making the decision to add a scene element from Anna’s internal motives, there is only one answer. “I see Diana. She lost track of time talking to the bartender.” Anna wants to see Diana safe and sound, so that’s what I want to be thinking about as a player. If you ask me what Anna wants, that’s what she wants.
“I see Diana” does not appear to answer the GM’s question here (“What do you see that tells you it’s a hive of scum and villainy?”). Is this an example of how you might answer a different question than the one asked, or just an oversight made when composing the post?