Has anyone ever seen one of these tiny vises?

Yes, I know it as an Engineers hand vice, typically used at the drill press when drilling small parts, especially if they are difficult to mount otherwise. They are also used by other Trades and therefore may be  known by a different name. And they come in various sizes.

It's a man's pair of tweezers... Or what smoggy said. Never seen one before but it would definitely be useful.

A hand vise, fairly common in the old days. The vise-grips have pretty much replaced them.

I have one in my tool kit, comes in very handy for small work.