I support the creation of a new tag for this. Once we figure out a good name for it, I mean.
That said, I'd prefer to keep it as a subset of animated (i.e. imply this new tag to animated) to keep tagging consistent with previous practices (i.e. if it's animated, it gets animated), to avoid needing to restructure the various implications to animated, and to avoid losing the animated "play" icon that shows up on thumbnails.
Edit:
evazion said:
Cinemagraph might be what you're looking for. A cinemagraph is a mostly static image with minor moving elements.
https://en.wikipedia.org/wiki/Cinemagraph
https://www.reddit.com/r/Cinemagraphs
Huh, this is right on the money. Might need a wiki rewrite and a utility alias though. And an implication to animated.