Pangram is probably the best known example of a detector with low false positives, they have a research paper here: https://arxiv.org/pdf/2402.14873. They do have an API but not sure if you need to request access for it.

For humans I think it just comes down to interacting with LLMs enough to realize their quirks, but that's not really fool-proof.

Pangram has time after time been shown as the only detector that mostly works. And that paper is pretty old now! There are recent papers from academics independently bench-marking and studying detectors e.g. https://arxiv.org/abs/2501.15654