Looking on the internet deeply has found these results:

have second thoughts is the most popular phrase on the web.

have a second thought 1356,000 results on the web	have second thoughts 1449,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	And I want to know if that made you have second thoughts about us. I don't trust anybody, and I'm starting to have second thoughts about this. Chicken. This subject is extremely important and it is natural to have second thoughts on such proposals. I'm starting to have second thoughts about him. And I'd be lying if I didn't say I was a little worried you might have second thoughts. I'm engaged to Tim though I'm starting to have second thoughts. But he told me that after 9/11, he began to have second thoughts. I'm beginning to have second thoughts about Taz.

have a second thought

1356,000 results on the web

have second thoughts

1449,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

And I want to know if that made you have second thoughts about us.
I don't trust anybody, and I'm starting to have second thoughts about this. Chicken.
This subject is extremely important and it is natural to have second thoughts on such proposals.
I'm starting to have second thoughts about him.
And I'd be lying if I didn't say I was a little worried you might have second thoughts.
I'm engaged to Tim though I'm starting to have second thoughts.
But he told me that after 9/11, he began to have second thoughts.
I'm beginning to have second thoughts about Taz.