So it turns out I had forgotten Yami does quote the something you can see but not see line to Jounouchi before: he does so in episode 6, as a clue to help Jounouchi figure out Mai’s trick,
referring to, literally, smell. Not his sharpest riddle. It’s cute that Yami helped Jou out, but it’s not really a touching moment.
Yami has a more touching something you can see but not see moment with Mai in episode 29, who heard Yami say it to Jounouchi and comes up with her own metaphorical not-card-game-clue answer
(and Jounouchi makes it weird)
Mai uses it to refer to her pride as a duelist; something invisible but that she clearly demonstrates.
But the original moment that makes these references meaningful to Jounouchi was a moment he had with Yugi alone and specifically about their particular friendship, because it’s from before Yugi solves the puzzle so Yami’s not around yet:
Jounouchi hears Yugi refer to the Puzzle itself as something you can see but can’t see, meaning it as just a cute little riddle when talking to Anzu about his favourite toy
And after Jounouchi makes amends for bullying Yugi, he tells him he treasures his friendship with him by quoting Yugi’s words
So I just think it’s sort of weird in episode 87 that the writers decided Yami, not Yugi, should be the one to encourage Jounouchi, and to do so with Yugi and Jounouchi’s friendship motto.
Especially because they had to switch places for Yami to do it; it’s not like he was already in control, it was a deliberate writing choice.
Although I think he might be meaning to refer to duelist pride rather than friendship here. It’s not actually very clear.
Anyway I know everyone would be a little confused and have friendship overlaps if they were friends with two different people in one body, especially since Yami himself didn’t know he was a separate person at the start. But everyone does know they’re different people now and I think the writers missed out on establishing other characters’ distinct relationships with Yugi and Yami.
Only really Kaiba and Anzu get noticeably distinct relationships with them; Kaiba’s rivalry and obsession are all for Yami and he’s quite curt towards Yugi (eventually graduating to a grudging respect), while Anzu’s noticeably more relaxed with Yugi and worried about both of them in different ways. But genuinely Jounouchi will switch back and forth, I am still very unclear about which one he thinks he’s promised to duel for Red Eyes, and he sees them just as much as Anzu does and has all the necessary information for telling them apart! They’re obviously both friends with him, but it would be cool to have the writing show them each develop their own friendship. I guess Yugi and Yami both play the same role in friendship with Jounouchi most of the time; a supportive duel mentor figure.
Anyway, it’s weird is all!