"Just ask the LM about itself" seems like a weirdly effective way to understand language models' behaviour.
There's lots of circumstantial evidence that LMs have some concept of self-identity.
Some work has directly tested 'introspective' capabilities.
This kind of stuff seems particularly interesting because:
Failure modes include language models becoming deceptive, less legible, or less faithful. It seems important to understand whether each failure mode will happen, and corresponding mitigations
Research directions that might be interesting: