I would imagine one making that sound of disapproval/disappointment with one's mouth. But that's because I'm familiar with the phrase. I'm not sure a lot of people are.
I am personally a big big fan of nuanced and subtle character actions, like say, sucking someone off your teeth. Clears throat These small gestures and actions are clearly human behavior , and are done sometimes in degrees and situations that connote or indicate mood and feeling. Let's use as an example the very same gesture you wrote in your post. And before I start, I'd like to make clear that I don't believe Spencer1990 grasps the mechanical movement of the tongue when sucking your teeth. I believe he is referring to the tsk! sound when one makes when: bringing the tip of our tongue behind (almost always) the upper incisors and pushing forward and off creating a tsk! sound. The mechanical action of sucking your teeth and not tsking is: bringing your tongue in between your teeth and (almost always) hugging the upper incisors while at the same time sucking in, either with mouth closed or open, the former producing no sound and the latter making sound. Now, before we get to the situation or what is happening in the character's environment or what that character sees, let's check off what this particular gesture connotes or doesn't. Have you ever had food stuck between your teeth? Ever have braces removed and had that urge to feel around? Perhaps you could cite just a few more examples but chances are that you sucked your teeth in those instances. Why? It's likely you did so because you had discomfort at food remaining on or in between those teeth or out of simple curiosity. So this doesn't connote or signify anything. It's just an action. But when it does connote a mood or feeling, it's usually easily perceived by or done in a way to make apparent. It could indicate impatience or irritability. Lust. Or annoyance at the cause of someone else. These are directed outwards. Sometimes inward. So when I think of, in my case, the gesture of sucking one's teeth, it's going to be negative. A parent at home or a boss in the workplace is sitting down with the erroneous one and that boss or parent is trying to make apparent that they are frustrated and begin with this gesture. I really hope this helps. It's something I'm always focused on. Thanks!
Imagine you've just eaten some fried chicken. A piece of chicken gets caught between a canine and premolar. You "suck" it out, rather than use a fingernail, toothpick, corner of a matchbook - "sucking your teeth." Some people develop this as a habit. Others use it as a sound of disapproval; tsk tsk tsk - like.
I forgot to come back to this thread. Whoops. Yes, when I think of "sucking teeth," I think of what was described in the last two posts. Hugging the upper teeth with the tongue and literally sucking on it, producing no sound, in a show of annoyance or irritation. But, upon googling, I found that most people relate "sucking teeth" with what Spencer described, making the tsk sound. So in order to portray exactly what I want to get across, I decided to ditch the description all together. Thanks everyone!
I imagine @Denegroth, or any senior member - leaning past his pillow at seven am. He reaches for the glass bedside, and plucks dentures from the water: And now the teeth inserted, he cries 'Jim Beam,' a baritone voice, and collapses back on the pillow for that extra hour of critical zzz.