To take action that is ineffectual and does not lead to progress. Refers to how a dog can exhaust itself by chasing its own tail. Come on, Bill, go to sleep. You're just chasing your tail at this point, but you might have a breakthrough with the research if you take a break from it. I'm trying not to chase my tail on this project, but so many components of it are just not working out.

slang To pursue or seek out sexual activity with someone. (Usually used by men to refer to women.) My brother always spends his weekends chasing tail in bars around town.