He decides to make a jump that could have killed him. For example.
And how did that develop/change the character? It is just another act of recklessness…
I’ll add to Mala’s point and say I don’t think he saw it as a fall that could have killed him. I think from the look of resignation on his face, he saw it as a fall he knew would kill him. I think it’s significant character development. He sees only two ways out: death or give in to Vader. It’s subtle in its execution (to the audience) but it’s far from the reckless kid we met in Star Wars. He’s willing (and attempts) to make the ultimate sacrifice to beat Vader and he makes peace with that decision. Nowhere near reckless.
Like I said, no matter how we call it, it is the same trait we have seen many times before. Attack on the death star was an “ultimate sacrifice” and he was basically choosing a very likely death too. When it comes to ESB, he basically made the decision to sacrifice himself already on Dagobah by going to face Vader in the first place. I do not see any significant change in character at all, especially after he decides to go for another one at the very end of ESB.
Now I am not saying that this any of this makes his character bad. I actually like it. It is just that his character does not develop a lot pre-ROTJ.
- edit - What Alderaan said.
Luke deciding to go with Vader instead of jumping would actually be a change of character.