2000 Cadillac STS code 1416 shows

What part did you buy, as there could be several possibilities. Bank 2 relates to the bank of cylinders that includes #2, which on your vehicle is the front bank. Are both air pumps coming on when you first start the vehicle, the air pumps are on the right and left sides, in front of the front tires. You can hear them make noise, but not necessarily tell if both are running or just one. If you have just one, I would pull the connector of the one that is not, alot of times there is a poor connection at the motors. You may also find that one or the other is physically damaged when you locate them. Check vacuum lines to the check valves, bank 2 is by the water pump housing. And check the vacuum switching solenoid that is under the engine cover, at about the center of the rear bank, it has a brown body and connector. That is a common place for vacuum lines to come disconnected.