Are there any theoretical properties of punctuation marks that allow to identify them without understanding the text?

Imaging that you have discovered a stone with written text in an ancient (or alien!) language that doesn’t resemble any known language. Is there a way to show that some of the symbols are likely punctuation marks?
How linguists would approach this problem?
The text is sufficiently long to test any statistical model. The direction of writing is known (e.g., left to right).