This separation of "sense of being" from thought also has been expressed in the teachings of Jiddu Krishnamurti, Sri Ramana Maharishi and Nisargadatta Maharaj. The writings of Nisargadatta are especially helpful in shedding more light on this phenomenon.
A very very corny way I like to think about this is the separation of the init process (being) from other processes (thought, sensation etc.). I know this is a very superficial interpretation, but I find it helpful.
Another corny metaphor I use for my mind is: Most of my thoughts are runaway processes that are just burdening my system. You don't want your CPU going at 100% for extended periods of time, same for the mind.
A very very corny way I like to think about this is the separation of the init process (being) from other processes (thought, sensation etc.). I know this is a very superficial interpretation, but I find it helpful.