My guess based on what had happened to me, is the vacuum line to the vacuum switch that operates the switch to the pump has perished and will crumble in your hands. A very cheap fix if you do it quickly. (Cost less than $5 at Autozone for vacuum tube.) If you leave it you could end up having to replace the Secondary Air Pump. (About $350 at Bavauto at the time.)
Check on RealOEM for a diagram of the SA System and you'll see the tubing.
GL.

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