An under voltage capacitor will have more internal resistance than the correct sized capacitor and might have a different effect on the phase shift between the winding's. It could also be a coincidence where some fiddling around the switch makes it work occasionally. But I would not use the under voltage capacitor in the circuit because it could explode.

Is this a pump motor that was working ok but has since failed or is this a pump motor that was just installed but never worked? A little history might be useful.