The first thing I'd do is remove the serpentine belt. Start the engine and run it for a minute or so (don't worry, it will take awhile to overheat). If the noise goes away, it's related to the belt, tensioner, or rotating components.

If the noise is still present, then remove the two hoses from the vacuum pump and run the car again. If the noise goes away, replace the pump pronto.

If the noise is still present after removing the belt and vacuum fittings, then my money is on a lifter. Perhaps it's periodic because the lifter is rotating.