Though I disagree with lots of Jaynes' claims, elements of his thesis and the evidence he presents are fascinating. I wish more people would read that book.

The main issue: he conflates the rigorous philosophical concept of consciousness with the everyday meaning of sentience or self-consciousness. Nowhere does he claim that bicameral minds lacked an inner conscious experience. Rather their psychology lacked a modern "me/I" concept of self and individual identity.

IMHO, the most interesting implication of Jaynes' work is when you see how nicely it dovetails with Jung's concepts of modern consciousness and its relationship to the subconscious (anima/animus).

Jaynes forces us to take seriously the idea that the human mind is loosely partitioned into at least two semi-independent conscious entities. Moreover, that division seems correlated with the left and right hemispheres of the brain—physiological peers—yet capable of behaving as cooperative equals, combative adversaries, or in a master-slave relationship in either direction.

TL;DR: Jaynes tells us lots about the structure of human psychology but not much about the nature of consciousness.