I love that, @MedievalMadness, and the related experimental work with 'split brain syndrome', examining people who've had the halves of their brain surgically separated (to treat extreme epilepsy). The theory of bicameral mentality proposes that ancient peoples didn't "consciously think" as we do, perceiving messages from their right brain as direct communication from the gods.
I'm not sure that theory holds 100% true, but it does make a lot of sense. Nowadays, we use different words to describe such things - instinct, gut feeling, spidey sense, having "the muse", being in flow - and, if we don't pray, we meditate, journal or get in touch with nature to achieve the same things.
So-called Third Man Factor was put forward in relation to extreme circumstances, but there are zillions of examples both life-threatening and mundane. A few people in the King's Cross fire "heard" or "knew" they should head further down, ignoring the official advice to go up towards ground level.
They tried to get others to follow them; those who did, survived. This is easy to explain from a distance - most of us know fire travels upwards, even if we've never actually discussed it, and regular commuters would have noted the staff doors & service tunnels, even if they'd never consciously noticed them. But in the emergency, those people "just knew" and, crucially, paid attention to what they knew.
It's what Gavin de Becker talks about in The Gift Of Fear.
I've had what I'd describe as massive posters appearing in my mind, telling me to take some urgent course of action, and I do "sense" various deceased relatives at times when their feedback would be welcome - and not (cheers, Dad, stay dead ... ) Also, I write. I never believe it's going to happen but, once I've started, my "writing voice" kicks in and comes up with stuff I hadn't deliberately thought about for one moment. Some people might consider that a spirit, and it is in a way - all coming from my own 1300 grams of squishy head organ, though.
It's a pity that fans of the supernatural here have been so angered by alternative explanations! I love ghost tales. My interpretation might be different from theirs, but why can't we explore the possibilities?