May be able to get them for less used, but a new taig headstock and tailstock will run at least a bill, and that's not including a chuck, pulley, motor, or any tooling to mount the cue. Then You can add the cost of 80/20 and the brackets on top.
To simply spin, for spraying a cue, you don't have to have something quite that ridgid, a simple spinning fixture is enough. The important thing is that You can control the rpm's. If you are wanting to sand on the cue also, then maybe a modified wood lathe could be had for cheap or the taig setup mentioned would be better. Not sure how well a sewing motor would work for sanding though. Depends on the motor I suppose. I have used sewing machine motors for other things. It doesn't take much to put a load on some of them, and I could sometimes see an arcing of the brushes through the vents, so proper ventilation aside, That is something that would concern me if using flammable clear. Water based or other non flammables not as much though.
If money is not an object, then the taig setup would be nice, I just feel that if It were me, I could put those kind of parts to better use elsewhere.