Ok, now that it's evening, I can take this more fully. Kaji's employer is only mentioned briefly in the series, mentioned some more in the manga, and only really clearly laid out in the Red Cross Book and other canon published materials. Kaji is a quadruple agent: A UN inspector who is spying for SEELE but who is really spying on SEELE for NERV but really working for the JMoI. Though as his suicidal last run shows, he's really just using all of that for his own quest for the truth.
Kaji's ultimate employer is the Japanese Ministry of the Interior, not SEELE. He's assigned to infiltrate NERV and find out what they're really up to, since the official story of Second Impact is known to be just that, a story. His cover is 'UN Inspector', and as such he is able to act as a public official, moving between NERV bases, checking out things like the Marduk Institute. This is what you see him doing in Episode 15, checking out buildings nominally being part of the Institute. In the course of his investigation, he uncovers the existence of SEELE, and somehow makes contact with Gendo (these two things are likely linked) and when in NERV-3 Berlin, steals Adam from SEELE somehow (You'd think they'd have ALL THE SECURITY on that) to deliver it to Gendo. This is the package he considers so important he ditches Misato and the Children and flies away when Gaghiel attacks the fleet.
He is trained as a spy and infiltrator, and does his job very well if he managed to snake Adam out from under Kihl Lorenz and SEELE. But there can only be a very small number of people who #1) know Adam even exists and #2) had access or even a chance to be near it. Once SEELE figured out it was stolen, they probably fingered Kaji as the culprit pretty quickly. When SEELE had Fuyutsuki kidnapped as a 'we known what you're up to' warning to Gendo, Kaji breaking in to rescue him is the last straw. Fuyutsuki even says so to him on the way out: 'This will cost you your life'. 'I just want to get closer to the truth,' Kaji replies. Gendo is sometimes suggested as the culprit for shooting Kaji, but I assess this as unlikely: He just rescued Fuyutsuki, and SEELE already knows where Adam has to have gone. There's no reason for Gendo to need to 'get rid of someone who might talk'.
When called on to settle the debate that Misato might have shot him, Anno definitively said no, it was a never-seen-as-a-character low-level gunman, not Misato.
Kaji didn't have a 'lack of interest in anything outside of his job'. He was in fact obsessed with discovering the truth behind Second Impact and the parties behind it, as a way of atoning for the failures that got his brother and friends killed in the aftermath of the Impact Wars. This obsession is what drives him to keep hunting, even when it becomes clear SEELE is going to kill him. That's what makes him leave what is basically an audio suicide note for Misato, and show no surprise when the killer appears. ('Yo. You're late.') He knew it was coming, and didn't even try to fight back.
Misato wasn't confused by his quest. She knew him too well, and by the time of the 'bedroom' scene, she's pretty much fully on-board with it. She's the one Kaji trusts to leave his accumulated discoveries and hacking tools to in that pill. That's the most heartbreaking part, and what makes Misato break down when she hears the message: She knows it means he's not coming back from this last mission, despite the fact that he and Misato had just gotten back together. He and Misato understood each other all too well at the end.
He's not surprised by Asuka's crush on him, though he is uncomfortable. She's half his age, and he's never gotten over Misato. When Asuka tries her clumsy, beer-fueled 'seduction' of him on the Over The Rainbow, his primary emotion isn't shock, its distraction: He has someone else on his mind, someone he's going to see tomorrow for the first time in years, yet who still consumes his thoughts. He tries to aim Asuka at Shinji, but mostly just ignores her attempts to 'woo' him, something that pushes Asuka to try ever-increasing tricks to get his attention, such as the 'HELP, I'M BEING KIDNAPPED! AAA!' phone call.
His 'seduction' shot at Maya doesn't seem serious. It mostly came off as a 'I'll see if I can sneak some MAGI access, but mostly annoy Misato who I can hear coming'. And Ritsuko (who clearly knows Kaji isn't being serious) is old college friends messing around (does Ritsuko look shocked or upset? Not at all, just amused), and again, annoying Misato. Why all the yanking on Misato's chain? Because even after 8 years, Kaji's never gotten over her lying to him about there being 'someone else' and her dumping him when they started to get serious. So he 'teases' her. Because to two emotionally scarred people like him and Misato, 'teasing' is a lot less frightening than being sincere.
To those of you hoping this was an update Alert, be calm: Update soon. 2000 words done, trying to wrap up the scene. Tomorrow, maybe.
