The first thing that comes to mind is, why is the pump cycling. The most probable reason is that the pump turns off when a preset vacuum level is achieved and turns on when the vacuum level falls off. If you remove the vacuum hose from the pump and plug the port (hold your finger over it), and the cycling stops, you have a vacuum leak or no accumulator tank. If it still cycles, the power is being cycled or the pump has an internal circuit to cause it to cycle.
If you have an accumulator tank and the system operates properly (air comes out of the right vents), it would be easier to just rewire the pump to run only when the AC is turned on if you have a slight vacuum leak and can not easily find it.
Gerald