You can test for runout with a small block of wood and a sheet of paper.
Most paper is 0.004", so thats a simple feeler guage.
Try to clamp if possible, the block to the table on the right hand side as you are facing it.
Set the corner of the block against the chuck or shaft and rotate the shaft several revolutions.
Now, while rotating the shaft, try to insert the paper between the wood and the chuck/shaft. Odds are you will find a gap.
You can fold the paper in 1/2 to get 0.008 etc etc.
One tip, hold the block on the right hand side as you are facing the chuck/shaft and rotate it in its normal direction (right to left).
I learned right quick if you spin the chuck/shaft into the block, it sucks that piece of paper in and enduces cuss'n.
Jim