Does it really seem to be, or do you accept that particular idea?
It seems to be.
You destroy brain, you destroy any sign of consciousness, soul, personhood etc.
Whether there is something that transcends this physical realm is beyond this physical realm's ability to ascertain.
Everything one can say about it existing, claim about it existing, is borne purely out of one's belief that it is so, not through actual evidence that it is so.
"Seeming" is an surely a matter of evidence: if there is no evidence it can not "seem" to be.
Without any prior knowledge, or idea of the brains activities, are there natural inclinations that lead to that conclusion?
Sure, there is the natural desire not to die, a self-preservation mechanism, that, in the absence of actual evidence of "life after death", creates the notion so as to assuage the concern one might have that this, this material realm that we inhabit, might be all that there is.
Could it be that the brain is a machine that processes our will, thoughts, and actions?
Sure.
It could be.
Just provide the evidence that it is, rather than being the machine that not only processes but also gives rise to those things.
Then, perhaps, we can talk about what "seems".
The term afterlife is misleading. It implies that the body continues to live. Or the person remains the same person, after the dissolution of the material body.
There is no afterlife, there is just life, for the spiritual soul.
That is just a matter of semantics and not really worthy of discussion here.
We are discussing the matter of what might continue after the apparent death of the physical within the physical realm.
Surely whether you wish to call it the afterlife, pre-life, part of life, continuation of life, post-life, life that is but is different to the life that was, or anything else, is an irrelevancy.
But as it is, you are also wrong: the term "afterlife" is almost universally understood to be that which continues after the death of the material body, whether in the same form or another (the properties of what might continue into any afterlife is of course up for discussion).
Without the body, the person can not remain the same.
So to say that it implies that the body continues, or that the the person remains the same person, is a mistake on your part.
But if you have any evidence as to what does actually continue into the afterlife, should an afterlife actually exist (and feel free to put forth evidence for the existence of an afterlife while you're at it), then please do.
Otherwise everything you say is simply a matter of your belief, not actuality.
And as such, in the absence of said evidence, please refrain, should you find yourself wandering toward that desire, from trying to assert your belief in any way as anything more than simply your belief.