The best learnt behavior I have is to slow down. In practice that means using phrases like "Let me think about that for a second", and maybe looking at or writing notes. As an interviewer, if anyone actually took a minute to think about what I had just asked them, I would consider that a huge positive signal.
Someone posted this Steve Jobs response the other day that demonstrates this well. ( https://www.youtube.com/watch?v=oeqPrUmVz-o ) . Even in front of an audience that size, there is no rush to answer. He takes quite a while to consider a response first. That said, he is still amazing at how he can have (apparently) a long narrative in mind as he starts to answer. I work with an architect who I can spring a complex qu…
As someone in a similar role – it's all cheating. They've seen a version of your problem so many times it doesn't feel new to them. While you were talking, the architect was walking down a decision tree of possible problem patterns. Every new clue you provided eliminated part of the tree until the only thing that was left were 4 options that you can eliminate or confirm by asking followup questions or doing followup investigation.
Once identified, you use the off-the-shelf solution in your brain. Slightly tweaked for the current problem.
That's what people buy when they hire for experience.