wompi2305

I have a spa builders ap1400 #2 hot tub with a waterway executive 56 side discharge pump that is having problems with the low speed coming on with the circulation timer. The pump works fine if started in high speed and then drop down to low speed but will not start on its own in low speed. I got this spot used so I'm not sure if the capacitor on the motor is correct or if the capacitor is wired wrong with both feet sharing the same run capacitor 55 microfarad. Both high and low speeds are on the same terminal and the common is on the opposite side. I've read some of these forums which state the capacitor is engaged with a centrifugal switch. I am familiar with motors having spent years in the field as a HVAC technician. Do spa pumps have a run capacitor on the side of them or start capacitor? Could I be losing voltage across the timer and that could be causing the problem? Any help could be appreciated