I came across this post and thought 'oooh, something I can finally help with!'
The "breeder" (in quotes because she has two clutches a year at most) I got Peach from showed us all her birds, was so enthusiastic about them. She had taught two of her parrotlets to wave on command, and also showed us the awkwardness of the movement compared to her Sierra Parakeets who were almost show offs in comparison (eating almonds....with their feet?! How dare they). It is very very cute though, this tiny little foot coming up out to one side.
While I haven't taught Peach to wave properly, I have attempted it, and she cottoned on quick when I put my hand near her as if for her to step up, then moved it away when she raised her foot, and rewarded her while saying the word wave (I really need to persist with that....). I believe my breeder also had a little wave hand signal for them, I doubt it would take long for them to learn that once they got the idea that lifting their foot up and when we say the word got them something yummy. Put it this way: Peach enjoys hanging upside down on her perches with one leg and wing stretched out to the side, like a little gymnast. She gets herself into the weirdest positions sometimes, so I'm gonna say that with a little persistence and lots of treats, there's no reason why they can't learn. They've got just the right personality so that if they could speak they'd be forever insisting they can do whatever the big birds can do, no contest