It's interesting to note that some time after writing this, Sagan became aware of the work of Jim Tucker, at the University of Virginia, attempting to validate the "past life" reports of children who've offered verifiable details in their accounts. Many children make such claims, but, as Sagan observed, “Young children sometimes report details of a previous life, which upon checking turn out to be accurate and which they could not have known about in any other way than reincarnation.”
I won't assert the truth of it, and I can think of a couple plausible vectors that don't involve consciousness surviving death and into another body (however unlikely they might be), but if it's compelling enough for the author of The Demon Haunted World to suggest it deserves "serious study", I'm the last person in the world to gainsay him.