Question: I agree that I am not different from Self. But there are good number of instances in which I get engaged with thoughts. Is this due to habit/karma? 

Yes, that’s it exactly. See these instances in the following two ways:

A. Each instance of engagement is actually an invitation to engage in citta suddhi (call this “mind or inner purification”). Accept, as far as A. is concerned, a teleological premise: each moment of “forgetfulness of the Self” (pramada) is actually strongly urging you to release this impurity.

B. Each instance of engagement is, more deeply, an invitation to turn inward “to check” whether it’s actually an instance of engagement. 

A. has to do with purification. It’s a provisional yogic teaching. (Some speak of “polishing the mirror until it’s spotless.”)

B., the deeper teaching, has to do with Self-abidance. In B., any vestigial belief about “sometimes” being “different from” the Self is to be investigated and summarily dropped. Is it ever true that I am separate from the Self?

We need both A. and B. until we only need B. Then, of course, we don’t need B. either. Why not? Because there’s only the Self, really.