I'm talking about a shop made alignment dumb bell either from solid, or from something like a section of tubing plus separate ends to economize on material. All you need is Loctite to bond the ends. Tubing is actually desirable because it doesn't need to be cut (stress relief) & has plenty of rigidity for this application. Once you have end blanks either center drilled & slightly oversize OD ends, you mount between centers (not a chuck or collet) & take a skim cut over the OD. Preserve that infeed setting exactly, flip the bar & repeat skim cut on other side. They are now centered and parallel. Indicating on the HS side & comparing that to the TS side will indicate in/out & up/down of the TS center. No cutting is ever required beyond making the test bar.
To check spindle alignment relative to bed, the best method I know of is a precision MT taper / parallel bar. The one I bought is MT3 so I use my MT5/MT3 ground adapter that came with the lathe. You can also use this to stick in the tail stock MT socket & do some referencing there independent of the headstock. If you have a completely parallel test bar, it must be gripped by a chuck or something & you introduce potential errors.