EzraS wrote:
if I tried walking in my tiptoes while flapping my hands, I'd probably fall flat on my face.

I can't say I've ever heard anyone claim they did both at the same time.
I've never specifically "walked" on my toes, but I do rock back and forth on my toes when I'm forced to stand in a que.
I've never overtly hand-flapped, but I do hold my key fob and flick my wrist up and down a lot when out in public, I think it's the same impulse.
The actual reality of these behaviors may not always fit the visual image you get reading about them - though I did know a kid in Junior High who did a classic nervous hand-flap almost constantly, it made him look like a big, gawky, awkward bird, like a spastic stork or something. Of course, I had never heard of autism back in those days, so never made a connection. I can only assume now, that's probably what it was.