Character Analysis
Gruff and humorless (a Tommy Lee specialty), and dressed entirely in neutral colors, Agent K (a.k.a. Kay) is the role Tommy Lee Jones was born to play. Seriously, flamboyant and flashy should not be on this guy's resume.
Kay keeps the citizens of Earth blissfully unaware that aliens live among them. He's saved the world more times than he can count. For his efforts, he's received no glory; in fact, no one even knows he exists.
If a fireman rescues a kitten from a tree, he gets a parade in his honor. Kay successfully managed the Zeronian migration of 1968 (oh, you didn't hear about that?), and what did he get? Nothing. Thirty years of that noise is bound to wear on a man's sense of humor.
Teacher, Teacher Give Me the News
Kay's main role is to be the mentor character, and just because he doesn't live as a hermit on a mountain top and sport a thinking man's beard doesn't mean he can't perform this role admirably.
Like said wise hermit, Kay introduces Jay to the realities of the world: Namely, aliens exist on the planet and live among us. In fact, he introduces Jay to this reality twice, first when he shoots Jake Jeebs's head clean off, only to wipe Jay's memory of the incident, and later with the worm guys in the MiB breakroom.
He officially takes on the role of teacher right after Jay's finished with his tests. Stopping Jay in the hall, he gives him his first lesson, a history about the Men in Black:
KAY: Back in the mid 1950s, the government started a little underfunded agency with the simple and laughable purpose of establishing contact with a race not of this planet. Everybody thought the agency was a joke except the aliens who made contact March 2, 1961, outside New York.
In providing Jay this information about his weird new world, Kay also teaches the audience. There's some odd stuff going on in this film: aliens disguised as pugs, cockroaches wearing human skin, and memory-erasing Pez dispensers. The audience, as much as Jay, needs a character to explain what's going on so we can keep tabs on all these bizarre happenings. Kay becomes our guide, too.
Another thing we should say about Kay's teaching method is that it's an on-the-job approach. Consider this scene after Jay's daylight shootout:
KAY: We do not discharge our weapons in view of the public.
JAY: Man, we ain't got time for this cover-up bulls***. I don't know whether or not you forgotten, but there's an alien battle cruiser about to—
KAY: There's always an alien battle cruiser or a Corellian death ray or an intergalactic plague that's about to wipe out life on this miserable little planet. The only way these people get on with their happy lives is they do not know about it.
First of all, when Kay gave Jay the Noisy Cricket, he didn't warn him that the gun kicks like a roided out mule. He just hands it to him with no instruction whatsoever, and that's not proper gun responsibility. Also, you'd think that he'd mention that the Earth being on the brink of destruction is kind of the norm, right?
Way to bury the lead, Kay.
But this hands-on approach seems preferable for Men in Black training. When Jay looks over the distressed faces, he learns that their mission is less to save the Earth from the aliens but more to save the sanity of the citizens, who aren't prepared to know that a movie monster is traipsing through their city. Plus, the containment crew can use their neuralyzers to hit the reset button on Jay's blunder, so no harm done.
It's also in keeping with the agency's necessary approach to the job. There are no canned response manuals for the Men in Black to follow; every situation is one-of-a-kind and needs a creative approach. Jay will need to think on his feet to become a full member, and the hands-on teaching approach is the way to foster this skill set.
Most movie mentors seem to prefer the hands-on approach. In addition to the above, the reason is that having the mentor character lecture in front of a chalkboard for half a film's runtime wouldn't make in an engaging adventure flick. Unless you can get Neil deGrasse Tyson for the role. That man could read a dishwasher owner's manual and make it engaging.
Man of Many Mehs
Jay's the audience surrogate, reacting with the same bewilderment we'd have if we saw half the stuff he does on the job. To provide balance, Kay acts completely indifferent to the strange happenings, making what would be Lovecraftian horrors in another film seem tame, amusing and even relatable. The result is that Kay enhances the film's comedy by being so blasé in the face of it.
When Jay and Kay stop Reggie, they find his very pregnant wife in the backseat. Kay goes to discuss things with Reggie while he has Jay handle the delivery. Kay learns that Reggie's taking an illicit transport off the planet because he "doesn't like the neighborhood" thanks to the "new arrivals." After Jay delivers the squid-alien-baby thing, Kay asks him in a deadpan tone, "Anything about that seem unusual to you?" It's the punchline to the scene.
Kay plays this role throughout the film. He's indifferent to the worms in the MiB breakroom, rocks out to Elvis while driving a rocket car on a tunnel roof, and retrieves his gun from the gut of a giant insect with all the intensity of someone making the office coffee run—which, admittedly, can get pretty intense sometime.
In each case, Kay adds to the comedy of the scene by being, ironically, humorless about the whole affair.
Love and Labor Lost
The final wrinkle in Kay's character is his past. Kay was one of the founding members of the Men in Black, and he left his entire life behind to support the agency's mission. We learn this when he tells Jay what he must sacrifice to join:
JAY: What's the catch?
KAY: The catch. The catch is, you will sever every human contact. Nobody will ever know you exist anywhere. Ever. I'll give you to sunrise to think it over.
JAY: Hey, is it worth it?
KAY: Oh, yeah. It's worth it. If you're strong enough.
This statement conflicts with what we learn about Kay later. Turns out, Kay left his wife to join the agency, and although he's kept tabs on her during his tenure, he hasn't contacted her in 30-some-odd years.
At the end of the film, we learn that Kay hasn't been training Jay as his partner but as his replacement. Unlike Dee at the beginning, whose "spirit [was] willing" but whose body was old, Kay decides that doesn't have it in him to stay with the agency any more.
As he puts it:
KAY: I've just been down the gullet of an interstellar cockroach. That's one of a hundred memories that I don't want.
We don't really blame him there; that's a memory we could all do without. But it's more than just forgetting about dissecting alien insects with an atomic weapon. After thirty-five years, Kay's tired. He's ready to go home.
And that's exactly what he does. Jay neuralyzes him and, as we read in the tabloid headline, gives him a happy ending, saying he's been reunited with his wife after being in a coma for 35 years.
In the reverse of Jay's story, Kay finds his place in the world but it isn't with the Men in Black. Instead, he finds it in the quiet life with a wife he thought he'd lost and a new lease on life.
Well, until the sequels need to find a contrived reason to bring him back into the fray.
Kay's Timeline