Experiences of non-local consciousness seem fairly common. For example, I once shared a dream with someone who later related it to me unprompted. I used to have a bagful of such stories, but I've forgotten them. I categorized them in my mind according to how verifiable they were. Third-part verification was best. I think if you go looking for such things you may find them. I suspect they tend to occur in groups where they're accepted, much like awakening and the DhO.
What that all says about death I don't know. Interesting to note, though, that fear of death is not the only complicating emotional factor. In Buddhism, fear of rebirth seems to get a lot more press. Somewhere on this forum there is a link to a concentration practice to recall past lives. Whatever you think of that, the point is not to prove your immortality, but, so they say, to make you properly afraid of rebirth. I've never found out what the preferred alternative is.
Also, I think we are sometimes discouraged from this discussion by peer pressure, scientism, and the fear of appearing to be afraid of death. I wonder if the tendency to discourage the discourse isn't partly a symptom of the limitations of "pragmatic dharma." Insight into death is not a fruit of our practices, whereas it is at least claimed in some other traditions.
I like
Bikkhu Bodhi's essay on the meta-discussion, although it doesn't give much in direct answer to the question of what happens when you die.
If we suspend our own predilections for the moment and instead go directly to our sources, we come upon the indisputable fact that the Buddha himself taught rebirth and taught it as a basic tenet of his teaching. Viewed in their totality, the Buddha's discourses show us that far from being a mere concession to the outlook prevalent in his time or an Asiatic cultural contrivance, the doctrine of rebirth has tremendous implications for the entire course of Dhamma practice, affecting both the aim with which the practice is taken up and the motivation with which it is followed through to completion.
Thanissaro Bikkhu has
an e-book that makes a similar case in more detail.