The articles you cited upthread do not support the notion that models consistently activate differently when generating true facts vs false facts.
It is true that models can capture some notion of reliability based on patterns in their training data. For a concrete example, it is entirely plausible that a model can capture the sense that data trained from Reddit is less truthy than data trained from Wikipedia, or that training data with poor grammar and vocabulary is less reliable than more sophisticated inputs.
But this process is not a guarantee, and does not change the fact that LLMs have no mechanism to track the provenance of information. It's probably a fruitful direction of research for reducing the probability of emitting false facts, but there will always be an infinite number of marginal cases for which the activations for true facts are indistinguishable from those for false facts.
Models simply do not track the provenance which is required to make this distinction in every case.
But I have seen issues with prompts where a creative-writing prompt and just asking a question look similar, and in that case it could help to know which one it thinks it's doing.
Gemini itself has a funny verification button where it more or less Googles every sentence the model writes and tells you if it seems like it made it up or not.