These are important techniques in a tense situation. Even in everyday conversations you can practice them.

I told the counselor that my mom could be too old, but I still have an opportunity to learn these techniques.

— 1) talk more slowly. Pronounce each word slowly.
This style is not so common, but not so rare either.

— 2) Pause after saying “Well, I think ….”, and think about what to say next.
Some great speakers simply pause for a few seconds.

You can do this after you speak or (more often) after the other person asks a question or puts forward a point. If the other person’s flow of words is not in receptive mode, then you don’t say this.

— 3) after the other person stops, wait 5-10 seconds for him/her to finish. If he/she has no more to say, then you can talk.
How about “hmm”? Not the same as the silent wait, according to the Cigna counselor.