I'm guessing that you would say a fertilized egg has a spirit, but are hesitant to say a "mere" egg does. Correct?
Yes.
Something like Jer. 1:5 is more typical though I would suggest that a just as reasonable interpretation of that verse is that it is an indication of God's foreknowledge. However, there is a verse in Psalms like "knit together in your mother's womb".
And Luke 1:41 also indicates the consciousness of the fetus. One can put together an impressive list of verses to support the fetus as a conscious being.
Neither of these verses though speak of spirit.
No, they don't. Recall that I marked our departure into speculation. Maybe I need to elaborate on that more. If I felt this were a Biblical principle, I would fight for it tooth and nail. Since it's just speculation on my part (shrug) I'm OK if it gets shot down. I'm at where I'm at because no one has offered me a better explanation.
However, we don't have any examples of mind existing apart from the brain for non-deities--so far as I know.
I'll give you more ammunition. Someone might suggest angels as another example (though, since you dismissed God as an example I expect you would dismiss angels as well). I would disagree that angels are an example of full consciousness. Though spiritual in substance (and therefore the essence of consciousness), I don't think of them as independently conscious.
Out of curiosity, supposing that you could be convinced that it was actually known and could be fully explained as a physical process: How would that change your views on personhood and conception?
My speculation is more material in nature than it is for many other Christians. Spirit needs a means for manifesting. The only non-material means is God. The material means is the human soul. So, the human soul is a physical thing. Whether it is just the brain or the entire nervous system or also the heart, I don't know. I suppose the sentimental part of me wants to include the heart as well.
And, with respect to the development of a fetus, they don't fully express their consciousness simply because the brain has not fully developed. That we cannot communicate with them does not take away from what they are - in the same way it doesn't take away from the personhood of someone in a coma.
The point is, I fully expect it to be a physical process. I believe it
is a physical process. It wouldn't change my view, but only confirm it. The aspect that separates me from the "scientific" approach to it all is my belief in the Godelian nature of it all.
How do I know you are a person? How would I know if an alien is a person? Are these tests applicable to fertilized eggs?
If you recall, I mentioned the viability argument. I was there for a time. At one time I believed people didn't have any spirit until after they were saved - only a soul. At one time I was not opposed to abortion. My mind was changed. From there I went to a "potential" argument. I suppose that is still where I am at to some extent, but neither argument works with someone who doesn't believe in spirit.
Regardless, this whole approach is centered in the idea that people have rights. Based on the way our legal system is set up, it's easier to argue for the rights of a fetus. But that isn't very Biblical. The more Biblical approach is one of responsibility. Intercourse means acceptance of the responsibility of the outcome.
So, whether the child is born or not is a matter of God's providence. My part is a responsibility to protect any child resulting from my actions. Their rights and personhood never really enters as an issue.
So, I don't have as compelling a need to define personhood as you do. That other humans are persons is a tautology. Beyond that, the Bible doesn't speak of any other souls expect for humans (and that includes Ecclesiastes). If the time comes when we meet conscious aliens, God will provide an answer for how to deal with them. It's an interesting question to ponder, but I honestly haven't put much thought into it.