Can you think of other examples, and the showbiz name for an actor having such a "signature"?

That would be their schtick...from the Yiddish, I believe.

>Others<

Jerry Colonna would roll his eyes.

You could say Chevy Chase's pratfalls in the early days of Saturday Night Live were his schtick.

Basically, schitck is a bit or device of physical signature (or "business") you incorporate into a routine or charcter (even your ongoing character's persona) to get a cheap laugh or a cheap reaction from the audience. Thus the old show-biz adage:

When all else fails, do schtick!

Generally frowned upon, nowadays, within theatrical circles as indicative of a lack of professionalism and/or integrity...however, the insider joke is that everybody knows they have done, and will tongue-in-cheekedly re-employ schtick whenever they can get away with it, which is whenever it works, 'cause, why not?