If it were mine I would measure the ring the headstock spins on to make sure the surfaces were parallel, thicknesses at several points with a micrometer. Then clamp he headstock with ring in it to as flat a surface as you can find, ideally a granite surface plate or table but a granite counter top, thick plate glass, cast aluminium tooling plate, largish milling machine table etc. Put the test bar linked earlier in the morse taper and check that it is parallel to the surface you clamped to. Rotate the ring 90º and repeat the measurement. In a pinch you could use a straight edge and measure to it. That will tell you if the bore the ring sits in is perpendicular to the bore of the spindle. If it is then you need to establish if the bed of the lathe is machined flat, ideally with a surface plate but a straight edge will work in a pinch. Sit the bed machined surface down on the surface plate and use feeler gauges to measure the gaps. Or use the same method with the straight edge. Ideally the straight edge would be the calibrated steel or cast ones made for the purpose but a good quality level like a Stabila would do. The biggest stumbling block for what I have described is going to be finding a flat surface to work off of.
With all the tools available with my last job I would have put it on a CMM (Coordinate Measuring Machine) and measured the heck out of it but with home CNC milling machines becoming more popular it could be probed on one of them. So if you do have a buddy with one you could enlist their help.
Pete