I presume this is an X move? If you have a really accurate straightedge/parallel, (like a granite Lab Grade artifact), set it level on the table, put a tenth indicator in the spindle, and do a couple traverses along the top of the parallel. You don't care about height changes, you're looking to see if the same ~.550" period is showing up as small movements of the needle.
Then lay the parallel over, align it to X, then do the same move with the indicator reading off the side. If you see movement at the same period it's likely something pushing the table either side to side or up and down as it runs. Dig in further to see what the mechanical issue is.
If there's no sign of mechanical movement, maybe this is a brushed servo and some of the commutator segments are more worn than others, introducing a motor speed variable?
Hopefully others will have better ideas.