Yep, Wy, I don't think there is a movement per se, with a name and everything... Joseph Garcia's book "Sign with Your Baby" has a lot to do with it, though.
The benefits are not just neural pathway stuff but early communication and lessening of toddler frustration. Babies can sign long before they can talk. The sozlet was signing from about 7 months old, could converse quite well at 18 months, with about 250 signs. (I wrote 'em all down... that's when I lost track.
) What was astounding to me is WHAT she wanted to talk about at that age... flights of fancy (she had long involved stories about the family of orange gorillas [orangutans, I figured out] who lived in our oak tree and had a pet fox), observations ("that girl is wearing a red hat"), etc., etc. Not just the basic stuff like "I'm hungry" or "I'm tired".
She is and was MUCH less tantrum-prone than most of her peers, and her verbal skills now are off the charts. That is usual with early signers but often levels off around kindergarten, but for now, people are often absolutely gobsmacked at what she says and how she says it. Multi-syllabic words, etc., etc. (She's almost but not yet 3.)
In other words, I highly recommend signing with HEARING babies, too.
(In the process of writing an article on this now.)