I understand soul as software of the brain. I think that was the original intended meaning, even if people didn't understand the concept well. I see no problem in saying your soul vanishes after the computer is switched off.
As I was saying both the Greek "pneuma" and the Latin "Spiritus" were originally quite literally "breath", even if some metaphorical extensions were added later. In fact both made a quite clear distinction between those and mind, e.g., pneuma vs psyke for the Greeks, and spiritus vs anima for the Romans.
The Greeks also weren't very convinced that you need a brain. (And the Romans pretty much left such matters to the Greeks anyway.) Aristotle thought the brain is what you'd nowadays call a radiator for the water-cooling system that (he thought) is your circulatory system. I still think he has a point, and some people only use it about that much
Earlier than that, the Egyptians were pretty sure that you totally don't need a brain to go to the afterlife. (Which I guess also seems a pretty good point, looking at some fundies

) That was the only organ they never embalmed. They'd just push a rod in through the nose, give it a good stir and pour it out.
On the other hand, the mummies and other suitable supports for the soul (seriously, it could also reside in statues and paintings) were prepared with the Ritual Of The Opening Of The Mouth. You know, quite literally so they can BREATHE. There's that breath connection again.
So as I keep saying, it was not about software running on the brain, but literally about that last breath. The pneuma or spiritus were literally that breath. The question it was supposed to answer wasn't if you're still thinking when the brain died, but the more brain-dead question: when that guy exhaled for the last time, when he stopped breathing, where did the Breath go?
Which, as I said before, strikes me as about as stupid as askling: when the clock broke, where did the Ticking go?