On the Rat is a more glorified example of On the Rag except in this case the test subject is not wearing a pad, or rag for the case, no, instead a tampon. The Rat comes into it because the string looks like a cute rodent tail hanging out.
Henry- "Man she dropped them jeans and I couldn't believe it. Her tampon fell out too!
Steve- "No way! She was On the Rat"?
Henry- "Yeah. Still did her though"