I've seen plenty of grafitti in caves but never seen any cave art. I have seen what people describe as historic signatures and dates. Today they are considered as historic but adding yuour own name is strictly frowned against and is illegal in a lot of places.
Yeah, or try carving YOUR name onto Register Cliff or Independence Rock; or draw a few lines on an unused part of the Nazca Plateau, and see what it gets you! No sense of humor.
The lower cave (the one which used to be open, but got sealed up by a rail line) under the "Ruby Falls Caverns" by Chattanooga supposedly has graffiti as you described, including (supposedly) Andrew Jackson's autograph. :')