The secondary air pump runs for a few seconds at cold start up. I'm not sure how or if it turns on with a hot engine. Have someone start it while you touch the pump. On mine, I don't think I heard it go over 45 seconds. When the pump starts to go bad, it will whine loud. You'll hear it sitting inside.

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'06 X5 3.0i - bought @143,123 miles (12/26/20)