Where is the air pump on a 99 mustang?

A 1999 Ford Mustang doesn't have an air pump in the traditional sense like some older cars with smog pumps. The secondary air injection system (which might be what you're thinking of) is integrated into the exhaust system and isn't a standalone pump with a easily identifiable location like a belt-driven unit. It's more of a series of components. To find the relevant parts, you'd need to look at the exhaust manifolds and catalytic converters, as well as the associated tubing and valves. A repair manual specific to your 1999 Mustang year and engine would be the best resource to locate these parts.