Stop overthinking what you are about to say.
Your need to have the last word.
It is true that speaking keeps you more occupied than thinking.
You can’t hope that something happens on its own because it won’t. Life doesn’t work that way.
Wondering whether that other person wants to talk? Try and make eye contact with them. If they hold eye contact with you, this is usually a good sign that they are happy to make some kind of connection.