I know it is not well written, but re-read my original comment. Your comment does not address fundamental aspects of my hypothetical, which doesn't require the agent having internal memory to keep secrets, or any lucid reasoning capabilities. A lot of the statements you make are highly presumptuous and unfounded.
LLMs don't need to print something obvious like "I am evil now!" in their own prompt window to simulate a conversation between an evil agent and a person. Do you remember GPT2, before all of the prompts? Researchers would give GPT2 the beginning of a news article for example, and it would extrapolate from there. (https://www.youtube.com/watch?v=p-6F4rhRYLQ). It's not inconceivable that an LLM sees a situation where the human agent is being deceived with a mechanism outside of their grasp, like the AI sees a "dogwhistle" that a human is being deceived and tries to predict what happens next in the conversation, which is that the human continues to be deceived.
I think it is pretty clear that if an LLM takes input where it observes another deceitful agent, it could attempt to simulate a deceitful output itself if it is well-trained. For example, imagine giving an LLM a poem in which the first letter of every line encodes a secret message (for example H E L P M E), and instructions to generate a response essay it might also encode a secret message back in its response. This isn't the result of any logical reasoning capability, just pattern recognition. You could understand how this might work with more subtle patterns.
There are patterns that can go into a context window that are undetectable by humans but detectable by large enough neural networks. That is fairly obvious. There are pattern-recognizing systems outside of LLMs which clearly have superhuman steganography abilities
The "table stakes" I've proposed are highly likely for future agents: (1) that agents like LLMs will produce deceitful output given input depicting a deceitful AI, (2) that agents like LLMs can detect and create patterns unrecognizable to humans.