The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with on second thought
Resulting from a revised opinion or change of mind, as in I thought I'd go to the movies, but on second thought I'd rather stay home. Similarly,
have second thoughts means “change one's mind,” as in I've had second thoughts about moving to Florida. This idiom alludes to ideas that come later.