I think its a pointer what you said there. "What thought doesn't separate?" I think it points you in a direction.
From what I understand (i will use my own experience as an example here):
Thought or thinking is a separation of "what is" or "the now moment". It fragments "what is" into concepts which are based on the past (based on my past conditioning).
This becomes very apparent to me for example if I watch myself meet someone for the first time, there is this looking phase of no thought, just observing for a second or two... and then thought sets in and begins doing its work (this person is quite tall, look at those nice eyes, what funny face this one has etc...) and I feel myself removed from the moment. Same thing when looking at a new car etc... No thought... then thoughts come in.
Another way you can notice this shift (or fragmentation of now);
Become present, go into the now moment (very little to no thought, dont create a mental idea of this, just slow down, breath, become aware, look without thinking).
Then after remaining there for a few moments, start thinking about something and watch as the now begins to slip away. Then start thinking deeply about something (a problem you have, something you really have to do and dont know how to do it) and watch and see your awareness of "the now" diminish or disappear.
Thought to me appears to fragment "the now" until I have little or no touch with it.
From observing myself and my family and friends I've realised I/we are trapped in thought (our own conditioning).
I think people like Krishnamurti and many others are pointing us in a different direction, away from the obsessive(or compulsive) use of thought.