It sounds like the speed control voltage (0-10V) is also powering a run relay. I looked at the schematic pointed to in your message and did not see anything obvious. It looked like there is a direction control relay on the BOB and the spindle starts and stops based on the 0-10V control voltage. I would have expected a run/stop circuit as well as the direction and the speed control voltage circuits.
Is the relay that you hear clicking when you up the speed on the speed control board or the BOB?
Are there any schematics available on the spindle speed control board?