What to do with your eyes
Once the phone is away and your face is back, there's a question people don't expect, which is what to do with it. The half-listen had a job for your eyes. Full listening has to give them one too, or the tug will offer one.
The answer is simpler than it sounds. Look at the person. Not fixedly, not in a way you'd have to think about, but as you would have before phones, which is mostly on their face with the normal drifting away and back. And let your face answer. The reason this needs saying is that a face that's been half in a screen for years has got used to being unread, and it can take a while to remember that it's the other half of the conversation.
Then have one thing ready to do at the end of a stretch of their talking. A question about the last thing they said. A reflection of it, "so he just didn't turn up". Or nothing but a nod, if the story's still going. The point isn't technique. It's that the eyes and face need somewhere to be, and the person in front of you is where.
Two earlier books cover this ground properly, and I'll leave it to them. You were waiting to talk is about listening with your reply already loaded, which is the eyes-up version of the half-listen. Let them finish is about coming in before the end. If you find that once the phone's away you're still not quite there, one of those is the next book. But most people find that with the phone gone, listening comes back on its own. The attention that was going to the screen has nowhere else to go, and it goes to the person, and the person notices, and tells you more, and the more gives your eyes something to do.
One small warning. In the first week, the full attention can feel intense, to you and to them. A partner who's used to telling you things over a lit face might be briefly thrown by being looked at. Let it be odd for a day or two. It settles into the ordinary thing it always was.