Since I've been weirdly dragged into this discussion.
Were I to try at any kind of an answer (I'm not a piano teacher, and so shouldn't) I'd probably ask the OP
Dinilup some questions. How do you yourself perceive rubato? How do you perceive it in connection with the piece your student is playing? If you see your student as talented, what specific abilities that he has right now can you draw on and expand on?
My personal experience with rubato:
By nature I am probably a singer, and the "singing quality" tends to come into things I play if they lend themselves to it and I let loose. It was all automatic, unconscious, and raw. When I first worked with my main teacher, he referred to my "cliche" - I always created this kind of stretch at the end of every phrase, which got tiresome and monotonous. My note values might be correct proportionally vis-a-vis each other, but it was hard to follow any kind of pulse, because I didn't have a sense of underlying pulse. That is one of the challenges of rubato: you want to get out of being metronomic, but keep the forward-moving rhythm that carries the music.
One element of rubato I learned with one piece was a gradual slowing down and speeding up without losing pulse. I used an imagery of an Easter bunny on skis going down one hill, up another, while regularly plopping out eggs.

It worked for me. Probably wouldn't for anyone else.
Another thing I learned turned out to be called "agogic accent". You might "meaningfully" delay the entrance of an important note, and oration works a bit like that - or a show: "And the winner is ... Whosit!" Or someone giving a speech, a lecture, a line in a play or movie, who delays or rushes a key word for effect. When I was learning to do this, I was plopping delays in weird places with weird effects, like a toddler who only gets things half right because she's learning and wildly experimenting. You need to get an idea of
why you want to do this to a note. Studying the score, and listening carefully to master performers to find out what they did with "time", and why, was part of the process for me.
And now I'm bowing out, because I have no expertise in this area.