Thanks for the tips chaps.
I finally got round to making a small adaptor to allow my finger DTI to be loaded onto my small magnetic base which is a handy thing to have. However, I managed to load the finger type DTI directly into a headstock collet and I positioned the stylus in the bore of the tailstock.
After a minor tweak, the front to back run out was less than +/-0.001". I tried moving the barrel to its maximum out, mid and retracted position and the same +/-0.001" was observed. All these measurements were carried out with the barrel and tailstock firmly clamped.
The vertical (top to bottom) run out is +/- 0.005" and it looks like the tailstock is 0.010" high. I will try removing it to see if there is any debris.
But even with this 0.010" discrepancy, I tried drilling some steel and it seems far, far better than it was. Before I made the adjustments, the tailstock chuck would tend to disengage from its Morse taper quite easily and start spinning in the barrel.
Thanks everybody.
My next task…. I'll check for swarf under the tailstock then finish off a rear tool post that I started ages ago.
Phil H