Matt, what kind of chuck do you use to turn a small button like that?
Usually, the same one I use for drilling on the lathe - either a collet (round blank) or pen jaws on a scroll chuck (for square blank). I make the button first, while there's still plenty of blank to hold onto. Then I part off the button and make the pen with the rest of the blank.
If I'm using wood with a pronounced grain pattern, I may prefer to turn the button "sideways" to show side grain instead of end grain. In this case, I'll usually cut the blank for the pen first. Then I'll take the cutoff end that I want to use for the button and choose the grain I want to show. I mount it in a 4-jaw independent chuck in my metal lathe with that face
towards the chuck. With the "back" facing out, I cut a tenon that will fit in a collet chuck on the wood lathe. (I use the metal lathe for this for two reasons: first, to keep my hands away from the spinning chuck jaws, and second because that's the lathe I have a 4-jaw independent chuck for.)
Then it's just a matter of putting it in the collet on the wood lathe and finishing it.
If the available blank piece were too small to do even this with, I would put a flat spot on it and use double-stick tape to mount it, but that has not happened yet.