Meanings
To grow a tail is a metaphor, as the anus where poop exits is adjacent to where a tail is placed. "Growing" in this case refers to partial expulsion as one attempts to prevent it.
to be nearly about to defecate, to the point of being unable to completely hold it in
Example Sentences
1
When I told her about the surprise party, she couldn't hide her excitement, and her smile seemed to grow a tail.
2
The little girl loved fairy tales so much that her imagination would grow a tail and take her to magical worlds.