hy
a fully programable tailstock can do all these from code :
... clamping/unclamping the part
... traveling to home position ( far right )
... traveling to approach position ( pretty close to part face, thus clearance position )
a manual type requires to be moved by the operator, maybe assited by the turret
if your tailstock looks like the one from attachement, and if after removing all those blue-screws, then is possible to rotate/translate it, then i can help you to align it at least in the plane that is paralel to the guides
if the tailstock needs to be raised / lowered, thus if it needs alignment in a plane that is perpendicular to the guides, then it would help if you would have an excentric sleeve inside your tailstock, and that, again, i don't know, maybe dhardt can provide a few ideas about how to do that on your machine
however, in some cases, the alignment in the plane that is perpendicular to the guides is required only if the head-stock was not re-aligned properly : thus if the headstock and the tailstock do not align in the plane that is perpendicular to the tailstock guide, and if there is needed to raise the tailstock, then maybe you should lower the head-stock instead ...
you have aligned the headstock, but do you know how far you are now from the original position ? for example, if your tailstock can be aligned in the plane that is perpendicular to the guides, only for 0.6mm, and your headstock is out of that field, then you are a bit in a tiny trap
to answer all those, is needed to align the tailstock axis at least paralel to spindle axis, and i can help you with this; after that, using a coax, you could see how far are those 2 lines from being coincident / kindly