The phrase “wandering thoughts” is interesting. Why not call the movement of thoughts “exploring thoughts”?  From the outside, exploration may look like wandering. From the outside, you can’t see direction; you can’t see what is being sought.  It’s all helter-skelter. The difference is that “exploring’ conveys intention or goal. As noted in prior posts, “stimulus-independent” thoughts are largely goal-directed and future oriented (Baird et al, 2011). When an observing part of the brain becomes aware of the activities of another part of the brain, the observing part may not grasp the latter’s business. Reference:

Baird, B., Smallwood, J. Schooler, and J. W. Back to the future: Autobiographical planning and the functionality of mind-wandering. Consciousness and Cognition 20 (2011) 1604–1611