Hello I will help you with your question,
If you hear the clicking with the HVAC controls and the fan in the OFF position it may be a relay in the cabin fuse panel. Pull the cover from the front of the passengers side of the console and feel the board there for vibration, To determine what is making the noise you will have to trace it by feel and possibly using a piece of hose to your ear to find the source.
Let me know if this happens with the engine and HVAC off but the key on and I may be able to help you narrow it down
The clicking noise can be heard with ignition on, engine not running, AC off, and recirculation off. The noise gets more pronounced when when AC and Recirculation buttons pushed on. I checked the fuses and fuse panel first. No relays in fuse box vibrating. The noise seems to be coming from under dash, behind glove box.
Your description sounds like the recirc motor is stripped and is trying to find home but cannot get there.
I am not finding what I need to show you about this system in the servive information but I will be home in about an hour and I have two of these vehicles in my garage so I will take a picture if need be.
Give me a little time and I will get back to you with the information you need
The recirc motor is mounted on the passengers end of the HVAC case, if you lay on your back and look up along the outer wall of the car you will see this motor and the connector going to it, if you put your hand on it you will feel the clicking.
The motor is mounted to the right of the blower motor, pulling the glove compartment will give you a little better access to replace the motor
The motor is available from a dealer or an ACDelco supplier (parts house)
Let me know if I am wrong about the source of the clicking or if you have further questions about this