I took a 3/4” diameter 24” long rod, nothing special, held it in a 4 jaw chuck with minimal stickout, adjusted for minimum runout and center drilled. Did the same to the other end, optional but seemed appropriate. Then I pressed a couple of about 2” diameter, 1” thick aluminum donuts on either end, about 2” in. Then center one end in the 4 jaw, other in tailstock center. Make a couple of light passes to clean up, and now you have a pretty good test bar where you can make a very light cut on one donut and without changing the tool position make the same cut on the other donut. If the two diameters match, your lathe is perfectly aligned. My guess is it won’t be, but you can get the error to a few tenths with some fiddling around.
Any feedback? Would appreciate any critique. It was cheap, didn’t take much time to make, but plenty of time messing with tailstock alignment, and let me see up close some of the surprising error sources when you are pursuing tenths.
Not sure about holding one end in a four jaw even if run out is zeroed. Isn't the tailstock alignment test supposed to be run between centres?