Which would tell you what, exactly? The whole root of the problem is that the model doesn’t “know” either

This is untrue and probably shows lack of experience with using LLMs. In my experience, each time I get some hallucination, I can ask the llm whether it hallucinated or not and I get a correct response.

> each time I get some hallucination, I can ask the llm whether it hallucinated or not and I get a correct response.

You get a hallucination of a correct response, yes, and given that it's a yes or no question, this hallucination is more likely to be correct than the response to the original more complicated question. But make no mistake that it operates under the exact same constraints