The key to characterization in Jesus Christ Superstar is that Jesus knows he is about to die the whole time, and Judas sees the signs but doesn't understand why they are happening. This might seem really obvious. But sometimes I see people confused about things like "Why is Jesus sometimes calm/happy and then angry for no reason?", and some productions that seem to fail to grasp this concept I think struggle in having a consistent characterization.
So from the beginning, Jesus knows he is going to die. He has his doubts (Gethsemane is nothing but doubts, and even on the cross, he says the famous "My god, why have you forsaken/forgotten me?"). But from minute one of this musical, Jesus is the person with a terminal diagnosis that they haven't shared with loved ones, and Judas is the one person who notices all the odd behavior (hey why are you spending all your life savings all of a sudden?) but doesn't understand why it's happening. And while the other disciples are more oblivious and willing to just go along with it, Professional-Wasp-Nest-Kicker Judas' fatal flaw is that he keeps trying to push for the answer or return things to how they were, not realizing that's impossible.
So we start with Heaven On Their Minds. Judas has recognized Jesus is acting differently, not addressing long-term consequences like Rome, but he doesn't know why. And the only reason he can think of is that Jesus has bought into the hype of his cult of personality. I actually think the 2000 movie plays this dynamic very well. Judas is begging Jesus for an explanation, and Jesus' facial expressions are very conflicted, like he wants to tell Judas but also feels he can't, he keeps hesitating, almost speaking, averting his gaze. (Which of course to Judas looks like just dodging the question). He keeps repeating "I just want us to live" which has to feel like a kick in the teeth for Jesus who knows he can't.
Then we have What's the Buzz/Strange Thing Mystifying. Jesus snaps at the disciples wanting to know the future because he doesn't have one. He encourages them to focus on the present because he won't be there to lead them, soon. He's conflicted, he's tempted to tell them, but he doesn't really trust they are paying attention or would really hear him even if he did. Especially when he's not 100% sure himself. ("I could even tell you where I'm going", "If you knew the path we're riding/you'd understand it less than I"). He lets himself be soothed by Mary because he's only got a few days left and desperately wants comfort of some kind. But to Judas, the guy whose movement is about helping the poor is suddenly using 300-silver ointment, which looks like he's just being wasteful, and again, buying into his own superiority. Not thinking about the future effects of being inconsistent or political crackdowns. I think the 2018 concert has a nice moment where Judas raises his eyebrows at the line "There will be poor always". Jesus knows he has only so much time left and he can't Fix Poverty. But to Judas, it just looks like more abandoning of Jesus' core principles. And again, Jesus can't help but try to warn him "You'll be so sorry when I'm gone", but Judas can't make sense of it.
Hosanna and Simon Zealotes/Poor Jerusalem are the wake-up call for both sides. One thing I judge productions of JCS on his having Jesus react in face and body language to the lines "Won't you die for me". He shouldn't be oblivious to it. (2000 also has a good 'I-told-you-so' expression from Judas). I love the 1973 movie, but every subsequent production that has the introductory instrumental of Simon Zealots involve an actual fight with the cops/authorities is correct. Simon Zealotes has both Judas and Jesus realizing some of his followers are going to push for a rebellion against Rome, and that Jesus can't stop them. But Judas' understanding of why he can't stop them is "Jesus has lost control" rather than "he won't be around anymore".
A lot of Jesus' songs at this point (his small verse at the temple, his reactions to the lepers, "For all you care" in The Last Supper" are him getting increasingly tired and hopeless, but simultaneously frustrated that no one around him sees or cares. (Judas both sees and cares, but does the opposite of help). Jesus' mood swings between calm (trying not to think about it), sad, afraid, and furious because he's essentially going through grief for himself.
There's a reason one of Judas' iconic repeated lines is "Every time I look at you I don't understand", Judas is getting increasingly lost and confused as he watches Jesus throw everything away with no apparent reason. When Judas' becomes aware of Jesus intentions is debatable. The Last Supper is a strong contender, as they literally argue about "You want me to do it". Here I have to shout out the 2005 Amstetten production. Judas his his absolute peak of confusion and desperation, grabs Jesus' face, begging "Jesus, please" just wanting an answer for all this self-destructive behavior. And then you see his face fall as he Realizes what Jesus wants and backs away in abject horror. (Though also arguably, Judas never fully believes in Christ's divinity and doesn't really see the scope of the whole plan until his own death.)
tl;dr: Jesus is mourning his upcoming death the whole musical and feeling alone because no one else knows; Judas knows Jesus well enough to tell something is wrong, but not why, and should play 90% of the show in increasingly hurt confusion.
