Those shooting gallery guns were BB guns that ran on compressed air.
They were not .22 short.
I had to look this up, it's been so many years ago and my memory is fuzzy.
But apparently you remember correctly and I'm wrong. The .22 were the pumps. And they went away even earlier.
Not what the OP asked, but if you built an air operated full auto - is this what the air soft guns people talk about are - that should be outside the jail bait territory wouldn't it?