Mike,
Aligning the headstock was the prelude to making a test bar and measuring the tailstock misalignment. I followed your instructions in your June 17 and June 18 posts, except that I made the test bar six inches long instead of twelve inches long. I didn't expect to succeed with the first one, and my projects so far have been on pieces less than six inches long.
I cut my 6" piece of drill rod from a 3'-long 3/8"-diameter tight-tolerance W1 tool steel rod (McMaster-Carr #8890K247). I made the machined section 1" long instead of your "maybe 1/2" long". I initially made the section 1/2" long, but that length required large tailstock ram extension to be able measure the diameter with my dial test indicator mounted in a Sherline insert holder tool post (#7600). For facing the ends and machining the section, I used a Sherline 55° RH carbide insert 3/8" tool holder (#2256) with carbide insert (#7605), as I don't yet have an adjustable tool post for mounting the custom "square" HSS tool bit that Jeff ground. (Cutting conditions for the section: 340 rpm spindle, 12.5 rpm z-axis leadscrew handwheel (0.0018" feed per spindle revolution); 0.010", 0.003", and 0.001" depth of cuts; and Boelube 70104-L machining lubricant.) The section came out adequately smooth.
I measured horizontal and vertical misalignment values across 4.4" of the 6"-long test bar. The values were 0.0032" and 0.0006", respectively. Here is a photo of my measuring set up, using a dial indicator mounted in the Sherline insert holder tool post (#7600) for horizontal, and dial-test indicator mounted in Sherline riser rocker tool post (#1288) for vertical.
Question: Are the horizontal and vertical misalignment values of the tailstock closer to 6"/4.4" times greater than what I measured? (multiplied by the ratio of the test bar length and the length that I measured across)
In doing this exercise, I came to realize that a dead center from Sherline can have significant runout. I measured 0.0008" TIR at the dead center in the headstock. The TIR varied between 0.0006" and 0.0010" as I loosened, turned, and reinstalled the dead center through 360° relative to the headstock spindle. (On July 16, I measured 0.0002" TIR at ID of the headstock Morse taper, near the mouth.) The misalignment values I reported above were measured with the spindle turned midway between the high and low points on the dial indicator (when the machined section of the test bar was at the headstock).
I didn't measure the runout of the tailstock dead center. I measured 0.0010" TIR on my Sherline adjustable live center (#1201), and 0.0002"-0.0003" TIR on my Sherline adjustable bullnose live center (#1205).
Karl