Folklore, Magic, & Psychic Abilities in the World of Pacific Rim
The existence of ghost drifting and drift hangover in the world of Pacific Rim implies that people have the potential to be psychic; that it's something that can be cultivated.
This raises the question of just how many ways one could potentially cultivate and strengthen psychic ability. Since the world of Pacific Rim is a very fantastical sci-fi universe, there's not a whole lot that's explicitly ruled out. And I think that leaves us with the question of what might be thematically fitting.
We could say that because Pacific Rim is an action-packed soft sci-fi flick, then anything from other action-packed soft sci-fi might be on the table. But I believe that to do this would ignore something that makes Pacific Rim special: its world is permeated and shaped by elements of myths, fairytales, and folklore that ultimately have origins in animistic worldviews.
The reason for this is simple - both Guillermo del Toro and Travis Beacham are deeply interested in fairytales, folklore, and the like.
In Pacific Rim, kaiju are effectively malefic dragons, associated with fierce weather events (in this case, hurricanes) and slain by heroic figures (Beacham even associates jaegers with Saint George). The Precursors fill the role of mysterious and sometimes frightful spirits thought to have their homes in realms beneath the waters. The character of Hannibal Chau owns an old-fashioned apothecary, and if you listen carefully you can hear a frog ribbiting in the background, as if to subtly suggest that Newt has entered the domain of an eccentric wizard.
Even Newt's prior kaiju drift experiment was nothing if not analogous to the many, many ways humanity has attempted to make contact with other beings, both those thought to dwell within our realm, and those thought to live outside of it. The act of consulting with unknown or untrusted spirits, or attempting to contact spirits in unconventional ways, has always been controversial throughout history and frequently banned by authorities (one of my personal favorite cases is when medieval university students were banned from summoning demons to help them pass their classes), but has never been entirely suppressed.
Based on evidence provided by Emma Wilby in Cunning Folk & Familiar Spirits, many people in pre-modern Europe engaged in practices that appeared to let them leave their physical bodies and visit realms where spirits of all kinds were thought to dwell, and that these practices very likely ultimately derive from pre-Christian spiritual practices. Newt's drift is not entirely unlike the sort of astral journeys described by Wilby; while his body remains in the k-sci lab, his spirit, so to speak, is able to enter the otherworld.
Emma Wilby also argues that fairytales about people visiting spirits in other realms are inspired and informed by the astral journeys taken by folk practitioners. And I can say this from personal experience: if you get into the habit of reading fairytales and mythology, one thing you will notice is how often somebody travels to an underwater realm, and how often the inhabitants of these underwater realms are some kind of serpent or dragon. (And a quick aside, it sure does happen a lot that these creatures are, shall we say, smoochable. The Shape of Water is riffing on old myths and folklore just as much as Pacific Rim is, just saying.)
In the context of Pacific Rim, Newt's otherworldly journey is facilitated by a piece of technology that allows him to directly link his brain with the brain of a kaiju. But if we permit the existence of ghost drifting and drift hangover, then we must accept that one does not always need technological assistance.
With the setting being so heavily inspired by fairytales and folklore, I think it's appropriate to look toward what magic practitioners in the past were doing. This well-cited post describes some things people did within Nordic cultures, including fasting before sitting outside overnight while alternately chanting and meditating in silence.
People have used more ritualistic means of contacting faerie spirits; such is written about in Knowing Demons, Knowing Spirits in the Early Modern Period, for example. While ritual magic does tend to have more complexity than the aforementioned Norse practice and is generally meant to bring the spirit to you rather than the reverse, they are nonetheless similar; they are frequently preceded by some form of purification (EG, fasting, abstinence) and use long invocations. The operator of the ritual likewise works in a state of focused concentration, and elaborate spoken incantations are generally involved.
I think it could fit the tone and feel of Pacific Rim if it were possible for people to eventually reach the hivemind through essentially a lot of focused meditative effort. I also see no reason why it wouldn't be possible to establish a sort of drift with another person this way, provided they had also cultivated this sort of skill. Perhaps two people could even cultivate this skill together.
In the case of person-to-person psychic links, I believe that Beacham's general sentiments about trust being fundamental would apply. It surely wouldn't work if you had two people trying to block or kick each other from each other's minds.
Additionally, Beacham's take on drifting implies that people can be kicked out of your mind if their presence is unwanted. Based on the parameters he gives, it doesn't seem like any sort of forced entry would be tenable. And of course, he also mentions that drifting only allows you to see what's currently on someone's mind - it doesn't allow you to search their whole brain like a database, so I don't think we'd see any psychics who can just walk into a room and steal everybody's deepest secrets.
If anything, I think a psychic person in the world of Pacific Rim might function a little like Miki Saegusa, who featured in several Heisei Godzilla films. The Pacific Rim film has a lot in common with these films, to the point I strongly suspect that they served as a point of inspiration. (Just read the page I linked, and I'm sure a few similarities will stand out to you.)
Another thing we could potentially throw in so long as we're leaning into folklore and folk magic, is the idea of premonitions and the like. Perhaps the world of Pacific Rim includes old grannies who can sense when a kaiju is coming.
Finally, the existence of drift hangover implies that humans have the capacity to imprint consciousness on things that otherwise would not be conscious. This is not unlike the notion making magically or spiritually animated constructs, or the concept of haunted dolls, or even some forms of talismans. Whether actual haunted dolls are possible within the Pacific Rim universe, or whether the potential to imprint consciousness is limited to sufficiently advanced AIs such as those found in the jaegers, is debatable and would, I think, ultimately come down to one's personal preferences as to just how magical they want this world to be.
Finally, there is the question of whether one could be potentially possessed by the Precursors/Masters, or even controlled by another human being. I believe that Beacham's interpretation of the drift as something that's only sustainable as long as the involved parties are willing to trust each other would make this rather unlikely. And while it's often assumed that the kaiju are effectively being puppeted by the Precursors/Masters, I don't think the narrative truly supports this.
While the film does describe them as being in a "hivemind," it would also appear that the kaiju are being instructed to attack rather than being puppeted. After his first drift with a kaiju brain, Newt describes the kaiju as attacking "under orders." Additionally, Scunner uses vocal communication to call for help when pinned by Lady Danger, an action which wouldn't make sense if they were all being directly puppeted by a single mind.
For all we know, the kaiju themselves might also have a bond built on trust - albeit, a very misguided trust in authoritarian leaders, rather than people who genuinely care about you. Perhaps they're told and believe that that death is temporary and they'll be reborn (taking a little inspiration from Hellboy here), or maybe they're convinced that they're serving a truly glorious cause.
Now, there are traditions that state that fairy can effectively replace a person; in Ancient Cures, Charms, & Usages of Ancient Ireland by Lady Wilde, a means of restoring a woman who has apparently been replaced by a fairy is given. If a woman is "nervous or hysterical" and doesn't recover, and the prayers of the priest don't work, a "fairy-doctor" might be called for; and if the fairy-doctor determines that she's been replaced by a fairy, will lay hands on the patient's head while reciting incantations. This is done over the course of three days. I think it's worth comparing this to an incident in another one of Guillermo del Toro's projects - in the Trollhunters episode The Exorcism of Claire Nunez, Claire's spirit is taken to the shadow realms while the spirit of Morgana is able to control her body.
With that said, I think it's very important to treat these concepts with some caution; the notion of possession has been used to dehumanize various people and justify abuse and hatred against them. (QAnon, for example, often does this to those they consider their enemies.) I personally have religious trauma connected to being accused of being possessed for basically being autistic and too opinionated for a "girl." The threat of possession was absolutely used to control my behavior, my interests, and all that. Because of that, I will personally never be able to feel okay with possession as Pacific Rim: Uprising presented it, with the guy who was too interested in kaiju getting possessed by their creators.
Finally, I would like to emphasize that the number of links and references I've given are actually pretty small in the grand scheme of things. The purpose is to give a few simple ideas of a few things people have done and believed, not to suggest that this is essentially all there is, let alone suggest that various cultures are or were basically all the same. There are absolutely loads of similarities between various mythologies, folklore traditions, and whatnot all over the world, but there are also a lot of differences, and those differences do matter. Doing more research could be incredibly helpful here - just try to make sure you stick with people who have actual academic qualifications (or at least heavily rely on those who do) and disregard anybody who's pushing conspiracy theories about myths concealing some "hidden truth" about our history or whatever. And of course, listening to people talk about texts and tell you about what's in them is no substitute for actually reading them yourself.