Be chasing (one's) (own) tail American British verb phrase
Used when someone is busy to do a lot of things but achieve little and do not lead to progress
I have been chasing my tail all day, but I haven't finished any tasks.
Used when one wishes to engage in sex with someone
They admitted that they were chasing tail in the bar last night.
The verb "be" should be conjugated according to its tense.
Used to imply that someone is acting as if he or she is demure, innocent, sincere or reserved but they may be not
Don’t be fooled by Jennie's good behaviour. She looked as if butter wouldn't melt in her mouth.