Do you have an MT2 collet or end mill holder that you can chuck in the spindle? If so, put a dowel pin or short length of drill rod, tighten everything up with the drawbar, and indicate off the pin or rod. That should get you close enough to measuring the spindle directly that you can determine whether it is the arbor or the spindle.
You can also indicate off the back of the spindle (remove the gear cover), a dial indicator on the inside of the spindle after you clean it, which should let you know if the spindle is true. If not, well, could be bearings, could be the felt washers used as spacers, could be a loose setscrew on one of the collars ... could be a lot of things. Fortunately the spindles are not too bad to take apart; the manual is very clear on the process.