I also often don’t have timely responses.

There are sometimes long pauses before my response or even mid-speech, during which I’m thinking about what’s said. But the delay is often interpreted as a cue for someone else to respond or change the subject, which often leads to not being able to say anything that i’ve spent so much glutamate to process.

I used to say “one moment” every 5 seconds while I think, but that was distracting.

Sometimes, I do this thing with my eyes jumping them around as if I’m reading a book; that gives people something to look at while they wait, like a spinner indicator.

As as over-thinker myself something I didn't appreciate until too late in life is the necessity of practice.

If you want to be able to hit a ball it doesn't matter how much thought you put into it - the learning is all about programming your lower instinctive brain and it only has the input device of repetition. This brain level has the ability to work at much lower latency - which is critical for reactive physical tasks.

I suspect it is the same here. You can certainly learn to speak using different levels of your brain as well. Case in point public speaking - the reason this is hard is generally you have to trust your mouth on automatic mode to follow behind and using the thinking part of your brain to better plan (or remember) ahead to build a narrative path.

There are body language cues that show you are thinking. Try looking up (like you're looking into your brain).