In a thread full of anecdotes, I’ll add another…
My father does this when he’s working on the car, a model airplane, or a computer. His goes up, like he’s trying to stick his tongue up his nose.
Why? I don’t know, I think I asked him once, and he was surprised to learn that he did it at all. I think it’s clearly subconscious behavior.
Most people seem to do it when their concentration is otherwise absorbed in a task. I recall reading somewhere (Discover magazine? Textbook? Google reveals nothing!) about a psych study that involved giving a student a list of question to do in order, where the teacher would then don a pair of headphones and begin marking tests. Of course, the test was missing page #2, and the data was how long it took for the student to interrupt the teacher to let them know about it.
Apparently if the teacher had their tongue sticking out, the average time went way up, so perhaps people needing total concentration stick their tongues out 'cause it works.
I’m shocked to find people actually do this, I thought it was just cartoon characters.
But then I bite my lips when thinking, so maybe it’s not that weird.
At the risk of a Hijack I wonder how many other weird habits people have when thinking.
Slightly different, people used to joke about me closing my eyes when I took a bite/drunk something. Apparently it made me look like I was advertising the food/drink.
I might as well throw in my anecdotes as well.
When I was a child, I would stick my tongue out when I was concentrating. When I had trouble doing a task, my father would tell me I wasn’t holding my tongue right. 
As I have grown older, I no longer do this no matter how intently I am concentrating.
On a different note, When I lacerated the shit out of three of my fingers, the hack that sowed me up, stuck his tongue out of the corner of his mouth while he worked. :eek:
My wag is that as you get fluent in a task, you no longer stick your tongue out, but you may do so while learning. Of course some people who are fluent, may continue to stick it out due to force of habit.