Tank, ESFJ (Provider)
This first one’s actually pretty easy. Tank is all dominant Fe (Extraverted Feeling). He shows great enthusiasm for his job, and when when he meets Neo, he proclaims, “This is a very exciting time!” He reacts with big facial expressions when Morpheus is taken down and Mouse is killed. He hugs Trinity and shares her grief after the death of their friends, and leads the mini-eulogy for Morpheus.
Tank also shows a surprising sensible side, revealing his Si (Introverted Sensing). “No one’s ever made the first jump,” he carefully reminds everyone when they gather to watch Neo in the Jump Program. And he’s quick to tell Neo that “This is loco!” when he decides to return to the Matrix to rescue Morpheus, reminding him of each of the hazards and obstacles that await him. Though he’s open and welcoming to Neo, he reserves his judgment about whether or not Neo is the One until he actually sees him in action during the helicopter sequence.
Granted, Tank skips the “major, boring shit” programs when he’s loading Neo up with knowledge, which is a little impractical and feels like more of an Se (Extraverted Sensing) behavior, but he probably just wants Neo to have a good time.
Dozer, ISFJ (Protector)
Hard to tell here, since Dozer has very few lines. He seems the sensible and practical type (Si), explaining to Mouse and Neo that the “goop” they eat is a combination of proteins and minerals that has “everything the body needs.” He also seems to work as ship’s surgeon, taking care of Neo when he first arrives with surprising gentleness for a big dude, so there could be Fe working there. ISFJ is just my best guess, though.
Switch, ISTJ (Inspector)
Switch doesn’t seem surprised when Neo doesn’t make the jump. “It doesn’t mean anything,” she says. And she’s very forceful with Neo when he wants to get out of the limo. “There’s only one rule here—our way, or the highway.” That sounds to me like an Si-Te combo (Introverted Sensing/Extraverted Thinking), making her an ISTJ. It’s entirely possible that given her fighting skills, she’s an ISTP, but she seems even more careful and deliberate than Trinity, so I’m going with Si over Se.
Apoc, ISTP (Operator)
Apoc maybe gets two lines of dialogue in the movie. He tells the garrulous Mouse to shut up at the breakfast table, and later hands Neo a gun and tells him he hopes the Oracle gave him good news. Almost zilch to go on, but given his verbal brevity and his apparent mechanical aptitude (he’s the limo driver, a good shot with a handgun, and one of the operators of the bank of gizmos that retrieve Neo from the Matrix), I’d guess first that he’s a Ti-Se combo, making him an ISTP like Trinity. But with slightly more breathable pants.
Mouse, ENTP (Inventor)
Did I say that The Matrix was anti-Sensor? Looks like the entire crew of the Nebuchadnezzar aside from its commander and its newest arrival are all Sensors. Mouse, on the other hand, is a non-stop fountain of Ne-dom. His Extraverted Intuition flies its flag proudly in the breakfast scene where he famously declares, “Maybe they didn’t know what to make chicken taste like, which is why chicken tastes like everything!”
That’s definitely an Ne-Ti combo, picking apart ideas and re-connecting them, and the way he instantly makes friends with Neo and offers him a “more personal venue” with the Woman in Red looks like tertiary Fe to me.
It’s a shame most of these fine folks got picked off by the end of the movie (Tank was replaced by the start of the next movie). I think I would have enjoyed the rest of the series better if they were all still along for the ride. RIP, Nebuchadnezzar crew.