Well, I was going to do a cleaning on the wetside but I've located the source of the chirping noise. It comes solely from the dry side.
As the dry side vibrates, I've noticed that it slowly migrates away from the rubber pad that it's sitting on. Another factor that made the chirping worse was when the electrical wire was pushed back, pulling the vortech slightly off from the pad. Even with the wire holder and few pieces of duct tape holding down the wire, the noise continues. The only way I've figured out that stops the noise completely is to push the dry side down. Any solutions?