Playing with eyes closed is something that I've never tried, but my guess is that it's forcing him to listen and that's why it works. (I need to try it myself!) What worked for me when I was a bit older is my teacher making me get a little handheld recorder (cheap ones were surprisingly good back then, and I'm sure the tech has improved). Try having him record the song and listen to the recording, and ask what he thinks. In particular, does it sound musical? Why or why not? My guess is that it'll reveal details he wasn't able to focus on while playing, and it will motivate him to fix them.
Closing my eyes really helped with removing all stimuli that distracted me from actually doing that and it made all the difference.
Feel the damn music :/
he puts heavy emphasis on practicing with your eyes closed from the beginning. this becomes possible through visualizing scales and chords from the beginning.
other aspects are: getting your ego out of the way, trusting in you inherent musicality and allowing you creative source to steer your fingers to express your emotions and avoiding conscious interference. there is also a lot of simple improvisation inside a chord from the beginning.
i cant speak for the long term success of his technique, but i like the approach and it makes sense to me with respect to other skills i have aquired before.
his youtube channel is a bit hard to navigate but this playlist is a good starting point: https://www.youtube.com/watch?v=TQxJJ7AgS7k&list=PL4cPpP-Ua6...
he also has a blog: http://piano-jazz.blogspot.com/p/water-pianism.html
He was an excellent teacher - one of the things he majored on was ‘blind’ familiarity with the keyboard. He would get you to close your eyes, then ask you to pick out, for example, all the Cs on the keyboard going up the octaves. Made a huge difference to my confidence in positioning my hands at speed…
I record and watch or listen after many days. I have recordings of some of my performances from years ago which felt really terrible on the day of the performance but felt ok many years later.
Each piece could be seen as many stories and as performer you can choose your story, then try to tell it. Classical pieces obviously have a canonical version which is what most audience would expect. Still, when learning such piece the story still needs to be there, not just as a sequence of prescribed pianos, fortes, and ritenuntos, but as a moving flow to capture interest and convey some relatable image.
I guess the classical training also can equip performers with such imagery. I have grateful memories of teachers that tried to project a story into our kid-minds before delving into technical aspects of learning a new piece. Very inspiring times.
So his teacher tells him to memorize the pieces. Good I think, so I have him go memorize each piece and give me a concert once a day. He's like 40% of the way there now, better but no where near close.
So his teacher now says go learn with your eyes closed. _This_ made the difference. He plays with the correct rhythm, corrects any mistaken notes because well mistakes compound, even his dynamics sound right now. It's actually beginning to sound like actual music!
For him I think closing the eyes got him out of his mentality of just rushing the pieces, it put him out of his comfort zone and that has made all the difference.