Aliging the tailstock

I'm going to need to drill a pipe for the hour hand on my clock.  But since I know that the tailstock on my lathe is misaligned, I could run into trouble since the pipe is 1" long. 

After a little examination, it looks like the headstock edge of the quill tube is about 1/16" down from where it should be.  (Seems like a lot of wear, honestly.  Maybe something else is amiss...)  It seemed like a small shim ought to fix the problem, so I put a small brass shim of about this size under the tailstock runner.

I checked the alignment with the live center just touching a rod I had trued in the headstock. 

I slid the shim in just far enough to get the vertical alignment about right, and then used the alignment screws on the side of the tailstock to correct the horizontal alignment.  This disrupted the vertical alignment, so I iterated a few times.  Being wary that the overall problem is that the axis of the quill is not parallel to headstock axis, I checked the alignment both with the quill retracted and fully extended before being satisfied that everything was in order.  This worked, so I think the shim does actually make the axes coincident.

I then marked the shim's location by scratching it with the graver along the edge of the tailstock.

To move the tailstock, I just have to remember to take the shim along with it.  Since the runners are well lubricated, this mostly means keeping a finger on the exposed part of the shim as I slide the tailstock.