Adjustment for tapered roller bearings is usually to give zero end float plus a small amount of preload.
That preload may depend on the construction materials (coefficients of linear expansion) and the operational temperature, to avoid any end float during normal operation.
If end float is the cause of the run out, it should be noticeable by deflection by side or vertical thrust on the shaft while measuring.
Horizontal cutters may have a slight run-out during operation, but this usually only means a slightly larger cut on some cutter teeth – to which you may become accustomed. – and is not generally over important in operation.
I'll now go and look at lathes dot co. These old horizontal machines are often overlooked (by vertical options) but have plenty of life in them (from a Centec owner), and are often of better quality than modern chinese 'equivalents'.
Edited By not done it yet on 04/12/2016 21:12:29