After 14 cycles, we're all very well aware of how important it is to smile with your eyes. On last night's episode, Tyra added to her tutelage, saying, "The smize is really just looking for something that you can't see."
So basically, according to this new instruction, "smizing" is exactly what I thought was all along: squinting.
Earlier in the episode, the girls were taken to one of the locations that Lord of the Rings was shot, and they had to pose in the doorways of hobbit homes. (So now that sheep and hobbits have been covered, what else is there for them to do in New Zealand? Track down Flight of the Conchords?)
Or as Tyra would call it, "Lord of the Rangs."