This was an interesting trig problem. I figured out that the centerline error is a function of the difference in jaw heights, the gap between jaws, and the diameter of the center finder tool.

For example, say the jaws differ in height by 0.01" and the gap between jaws is 1":

center finder diameter error in centerline
1.1" 0.002"
1.5 0.006"
3.0 0.014"

This tells me that for the best accuracy, you want the center finder's diameter to be as close to the gap as possible without falling in.

Rick