> You can have introspective access to these brain processes.

Yes and no.

If you take a look around you, you could see a lot of different things. But there are no things around you, there are some quantum world, photons going in every direction. It is your visual system process signals from your retina and creates images of things, and you believe that images you see is a things.

The same story is with brain processes. You have some kind of images of your brain processes and believe that this images are brain processes. The more you meditate the more you extend mapping between processes and images. But it is an illusion. We could safely ignore this and we could believe that images are processes if the mapping between brain processes and images was isomorphism. But it is not.

All your understanding of yourself is a simplified model of yourself. It is like if you try to describe how works some neuronet and why it outputs A when you feed B into it. In your explanations you can refer to training process or to "features" that arrive at different layers, but it would be artifical explanation, because really neuronet outputs A because it outputs A, the only way to check this fact is to run a neuronet or make a simulation of it.

If you think that you know how your brain works, then try to make simulation of it, you'll see that you don't know how it works. It is like brain visual processing which seems easy and transparent process, but if you try to reproduce it, you'll find that you don't know how it works, and the only way to reproduce is to create artifical neural network and to hope that your model of visual cortex captures all the importand details.

Your thought process is a black box, but you are so used to it, that it becomes transparent to you and you cannot see it. Like you do not notice blind spot on your retina. Or maybe it is more like your eyes, which you cannot see because you see through them.

> If the subconscious can't think, tulpas, which maintain personality distinct from the normal operating consciousness, would have nowhere to 'hide'.

Your conscious is some kind of mapping of brain states into domain of abstract ideas like "belief", "thought", "emotion" and so on. You have beliefs, thoughts, emotions, you experience them as the primary entities, but they are not. They are just an outputs of function applied to brain state.

So why mind cannot have two mappings that exists simultaneously? It is easy. Look, lets B(t) is state of your brain. Let Y(B(t)) would be mapping from B into your consciousness (or, I think, it would be better to say that Y is your consciousness). Let T(B(t)) is the consciousness of tulpa. Now all you need is to make T(B(t)) to be a part of Y, that would convert inner state of consciousness of tulpa into visual and auditory representation of tulpa in Y. Mappings themselves are hidden from you and you cannot "see" how they works, they are invisible black boxes. You can "see" only outputs, or their outputs is what you "see" as conscious you.

By this way there are thoughts only in your consciousness. Tulpa have no thoughts, it is you use idea of "thought" to explain behaviour of tulpa, like you use idea of "thought" to explain behaviour of youself.