"Have a thought" is correct.
I have a thought about where we should live. (Thought=idea)
Have a thought about the poor mice! (thought=concern for)

"Have a think" is a humorous colloquial expression or else bad grammar. "Think" is a verb, not a noun.
A grammatically correct sentence would be:
Think this over.
OR
Let us think about this.
Depending on wh

"have a think" means to ponder or consider something. "I don't know the answer to that. Let me have a think."

"have a thought" means to have an idea. "I've had a thought. Suppose we try to do it this way ..."

Doctor D"Have a think" is a humorous colloquial expression or else bad grammar.

Hmm, well perhaps there are regional differences. In the UK "have a think" is a normal informal expression.

I feel Winnie the Pooh has said that at least once.

GPYHmm, well perhaps there are regional differences. In the UK "have a think" is a normal informal expression.

I rarely hear it here. I believe you also say "have a lie-down", which we don't use much either.

CJ