That "click" is a sound I think every grey makes if it is what I think you are talking about. I've seen several different "interpretations" of it on the forum. Check out the "stickies" on the first page of the forum. There is a lot of useful information there. For Timber, the click seems to mean a couple of things. We call it his thank you, since he often does it after we give him a treat. He will also do it when he wants my attention sometimes. I've seen it listed by some as a warning, but in Timber's case that doesn't seem to be the meaning.
Most greys love to whistle. When I was trying to get Timber to interact initially, I started whistling to him. Before long he was whistling back. I still whistle to him often. When I am in another room and he can't see me, that's how we communicate and I let him know my location. When I get up in the morning (I'm upstairs, he's downstairs) as soon as my feet hit the floor he will start whistling. You'll also probably notice a particular whistle/sound pattern your bird will often make. That is his/her contact call. Birds are flock animals, and the contact call broadcasts their location so you can find your way back