The truth Zen that points to is always present, closer even than our own breath.
We don't awaken to interconnectedness, as it is sometimes named, for that leaves an intellectual gap as we think about interconnectedness. As in, "Wow, look at how the war in Antarctica affects ice prices here in America." Rather, awakening is seeing that we are that very interconnectedness.
We aren't a being connected to other beings, as much as we are the ever-fluid connection (of everything) itself.
The Buddhadharma is always transmitting itself. We and all beings are that very transmission. This is how Zen goes beyond birth-and-death, not as the realization of some metaphysical entity or soul that transcends our body and transmigrates after death. It's the recognition that our minds appear in this sea of temporary appearances, remain for a while, and then diminish. Human consciousness is not some eternal principle that is somehow more important, privileged, or even fundamental than flowers and rain and electrons. That view, in Zen terms, is picking-and-choosing.
Consciousness is the natural result of the vast matrix of interconnection. It's another feature of the universe like mountains and rivers and trees--an awesome and magnificent one at that, but then again, so too are bees, mushrooms, and black holes.
The Buddha mind isn't the discovery that we are actually immortal Consciousness, but, paradoxically, the realization that we are finite minds and bodies with expiration dates; yet because of our inseparability from everything else, we are deathless. As expressions of the totality, we cannot go anywhere because there is nowhere for us to go. There is no "I" to go anywhere.
Dharma transmission from teacher to student isn't the transference of knowledge or even the acknowledgement of special wisdom. It's more like two old friends sharing a joke. "So that's what all of the masters were about," followed by a full-bellied laugh.
Special thanks to my teacher and friend, Wonji Dharma.