It's the whole activity, not the inner experience someone has while doing the activity. Who we are when we sit is not something that's going on inside our heads. It's the whole activity of sitting together in the zendo, it's our bodies, the other people in the room, the city where we live and practice, the long tradition that has taught us what we're doing here. One thing that is going on, of course, is that we think as we sit. But it's just one thing - along with physically sitting still, itching, listening, getting up at the sound of the bell and so on.
Thought is just one dharma, one event, among many.
That's one reason we give our attention to ritual and procedure in the zendo. Who we are is how we do all these things, not just how we think or feel while we're doing them. Let them come, let them go. Just sit with it all. Just be it all.