I generally don't expect the other person to stop talking just because I start - that was the way I communicated with my siblings and best friend (talk and listen at the same time) and it was jarring at first to have people interpret that as rude, and/or to stop talking so I could.

I don't have anyone left in my life to talk like that with, and I CAN listen without talking, it's a skill worth developing I think, was always necessary for deeper conversations, but listening carefully is, I don't have the right word but somewhere between polite and caring. Not listening with everything you want to respond top of mind.