My cockatoo does this when showing off, happy, sassy, sexy, over-stimulated...it's a mixed bag LOL! 99% of the time for her, it is enthusiasm of some sort. I know it's not intimidation in my specific bird--cockatoos are relatives of cockatiels and I know a lot of Toos click. A light clicking for mycockatoo (like a quiet 1,2,3 pattern) is a contentment thing. They other (louder) stuff is playful or rambunctious-- mine does it when she is being silly and is all wound up/happy. Dunno if that helps you with your tiel...but wondering if it is similar.
Here's what I found on a website (I will say with certainty though that my cockatoo has NEVER used this when trying to keep me away...so maybe she's just weird)
"Clicking: Beak clicking is usually seen in cockatiels and cockatoos. If your parrot clicks once and pins his or her eyes but is otherwise unthreatening, your pet is greeting you or acknowledging something. If, on the other hand, your parrot clicks several times in a series you should consider this a warning that your parrot does not want to be handled." <--again, my too does it when she is being a clown...and seeking attention, but she may be the minority