I often do this in meetings and have gotten into the habit of saying "I'm thinking". It's not much but it gives both of us time to think and explicitly makes it clear I don't expect the person to say something. I think that helps.
Fair enough, I do like parent’s a bit better, “blurting processing” feels like a too high default setting right after seeing “I’m thinking” :) - not that any of it matters anyways, communicating _something_ gets you there. Rest it just triaging around the edges what people will call you weird for, and if they are, they were going to anyway.
"Give me a second" is something I say when someone just has to break the silence with some unproductive comment. Having 20-30 seconds to think silently should be a completely normal thing.