I think this is what Socrates was talking about when he mentioned that he had a daemon within his mind that guided him throughout his life. Jordan Peterson has also articulated that this idea was also expressed in Pinocchio, embodied by Jiminy Cricket. He has also expressed that when he was young, he heard a voice in his mind that told him to act morally and pursue the truth. Carl Jung mentioned that the "Self" was the unification/integration of the unconscious and conscious minds.
We modern people will call it "conscience", but I highly doubt if we'll ever get to understand what it is. I don't think it is a phenomena that can be captured or explained through empirical means (or at least, not with our current technology) - similar to the idea of a soul or spirit. Perhaps we shouldn't even try to approach it with such a reductionist mindset - the moment we say we "understand" a phenomenon, we put rationality on a pedestal and demean all other possible explanations. But I can see that if we cease to explore and explain the "unexplainable" phenomenas of this world, we close the door to possibilities of a deeper understanding of ourselves and the origins of our minds.
The fact that people from all over the world believe in the existence of God means that it is a shared experience for all humans. But we all give different names to such a phenomenon. Are we all talking past one another? Why are we killing each other over what may, at the end of the day, be the same God that we all know and serve (willingly or unwillingly)?
I'm still searching for what God is to me. I'm sure that it will take many life experiences and perhaps the rest of my life to come close to understanding the phenomenon of experiencing God. But I'm glad that I've done away with the New Age Atheist attitude of discarding the idea as a simple, superstitious idea. Jung said that "modern man does not see God because he doesn't look low enough" - elevating ourselves to become gods and having nothing to bow our heads to may have dire consequences (and have had dire consequences, as we've see the rise in atrocities and inclinations for totalitarianism in the last century).