You would have to train it/finetune it on a couple hundred of 'humans chatting in the context of a Turing test'.
However such good conversational agents would still have benefits, and i would be curious how far the approach of building a model that’s nice to talk to can take you, as opposed to the current generation of all-knowledgable helpful assistants.
The big problem with the Turing test always was that it doesn't take into account adversarial designs. They had those chatbot contests about a decade ago, where the chatbots would regularly pass the turing test, not because the bots were intelligent, but because they were packed with rhetorical tricks designed to avoid saying anything of substance.
By any meaningful measure, today's LLM's pass the Turing test. Except we may need to lobotomize them for the deception to work.
What's more interesting are the types of humans that might fail the Turing test. Maybe to discourage the failure of real humans, there could be consequences outside the context of the test.
That is, most people accused of being a computer would crack and start pleading their humanity, but some sociopaths might not. I then wonder how many of them overlap with those so invested in abusing the premise of the Turing test.
It really is a fun thought experiment when you spice it up enough.