When working up the details of the antiinnatia theory, it very soon became apparent that some features of autism could not be credibly explained as due to simply loss of innatons. This led me to think of the idea of prehuman innnatons being suppressed by later suppressing characteristics, and indeed I thereafter learnt that this concept was already well-established and called atavisms. I explained the handflapping and posturing as a re-emergence of the sort of behaviour regularly seen in wild rats, squirrels and birds in the wild. Fuller details are in the 1993 paper.
Nowadays with the internet it is vastly easier to research things than it was back in the 1980s and 90s. I have now learnt that we did indeed have a rat-like prehuman ancestor, for 163 million years! As indicated in this video of your granny (which be warned is rather 'exciting' by the way):
same as at:
P.S.: The palaeontologists have not presented a very accurate image of the rat-like behaviour here. Just watch any squirrel or bird (in the wild) to see what I actually had in mind, and which surely would have applied as a defence against dinosaurs.
Meanwhile, in this charming video, eight-year-old Anthony seeks to describe his (and others') stimming (by which he basically means handflapping episodes). Note that he emphasises that it is liable to involve getting up and moving forward, which rather agrees with my theory's explanation of the handflapping as an atavism of the rat-like behaviour of our ancestors, as per Purgatorius video above. The point being that this shows some remaining trace of (hind) legs movements and forward movements as per the original function of the hypothesised innatons. Note in my 1993-published paper my explicit assumption that the handflapping did not have any related leg movements (because I was only going on the information I had at that time).
I should add that Anthony's attempted simulation of hand-movements does not correspond very well with actual videos of handflapping, which do indeed look suggestive of the rats' sprinting movements. For instance you can see (at 1.56) in this video of the Minamata disaster a more typical example of autistic handflapping, in this case seemingly caused by the mercury from the Minamata pollution (so best pretend you've not noticed it if you work for the FDA, CDC, NHS etc). And immediate before that you can see a cat doing something remarkably similar.