It isn't loadbearing, so to some extent this is "Just do it."
I Am Not An Expert, but my semi-educated approach would be to frame it in a 6.5' section over an 8' section, or some such division... not least because that would make wallboarding it easiest, and it avoids having to buy and handle longer (more expensive and more awkward) lumber.
You'll have to open up ceiling and floor to attach the wall's top and bottom plates to the joists, and maybe some of the wall so you're attaching properly to studs.. Frame in the bottom as if it was an 8' wall with its own top plate with 8' studs 16"-on-center, toenailed at the bottom and nailed through at the top. Then that plate becomes the bottom plate of the next section, whose studs get toenailed top and bottom.
Remember to frame in the doorway when working on the lower section, of course.
(I'd be tempted to put a decorative window somewhere in this wall, just because I like 'em and because that tall a wall cries out for something to break it up visually... but that would complicate the framing, and you may have other plans for that surface. I'd feel more strongly about it if there were windows over that stairwell, to avoid losing as much natural light.)
Quick thought: If you can put a screen, or bookcases, or something (cardboard? blankets?), along the proposed line of the wall that'd be a way to live with it for a while and check that you really do want to do this. You might decide that the resulting traffic flow isn't optimal, or that this makes the living room feel too closed in, or something of that sort. Yes, a nonstructural wall can always be taken out again, but it's better to make sure you have a reasonably clear vision of what it will look like before you start. Among other things, this is going to impose additional limits on what can go up and down those stairs -- having had to fight a 7' sofa around the bends of a twisting staircase, I'd be nervous about having that narrow an approach to them from either direction. Even if there will be a high ceiling so you can tilt things on end.
(Personally, if I was modifying that space I'd be more likely to put in a landing at the top of the stairs, with a railing, looking down into the great room. But I assume you want the wall either because you're subdividing the house or trying to block airflow.)
Afterthought: Have you thought about lighting for the new stairwell corridor?
Second afterthought: Make VERY sure that the studs are as plumb, and in line with each other, as possible. Failing to do that will result in one part of the wall being tilted relative to the other, which may not look very good and be a pain to disguise.