1
general::
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. [Mid-1600s]
American Heritage Idioms
2
general::
Phrase(s): on second thought
Fig. having given something more thought; having reconsidered something. • On second thought, maybe you should sell your house and move into an apartment. • On second thought, let’s not go to a movie.
McGrawhill's American Idioms And Phrasal Verbs