In an out-of-body experience, what part of the mind is taking and witnessing the excursion?

This is the upper subconscious, and the tell is that it will recall the experience and can, under the right conditions, even describe what it is perceiving to outside observers. So even though the consciousness is out and about and might be far removed from the physical body, it is still tethered and can connect with and even, under the right conditions, speak through the physical body to communicate. So this is an attribute of nonlocal consciousness coming from the upper subconscious level. The deep subconscious stays within the being, as it is the fundamental anchor of things. It uses its own gateway to access the akashic records, for example, and so is very adept in going beyond to repositories of consciousness and can interact with other beings, in fact. But it is done through nonlocal consciousness rather than a true out-of-body excursion in the sense people have experienced, where they can essentially pop out of the body and float about, hover above their physical self and look down and observe what is happening in the room, and so forth. This is the mechanism of the near-death experiencer going outside the body and perhaps going down the hall into a waiting room and seeing their loved ones worrying about them, while they are being resuscitated back in the emergency room, perhaps, and truly in an in-between state at the border of life and death. It is nonlocal consciousness at a higher level of the mind than the deep subconscious in that instance as well, and that is why it can be more readily remembered and make an impression on the experiencer. If this were done by the deep subconscious, the higher levels of the mind would have no way of knowing at all and could not describe the experience.