This is perhaps the most ambitious and contentious headcanon I have, namely because people love to imagine that the Links stay separate somehow after their adventure or that Link has dissociative identity disorder after his adventure. I don't like the DID headcanon because it is never based in the actual nature of the disease, which is typically that it manifests at an early age due to childhood trauma. I am not anti-endogenous systems, as there are documented cases where DID manifests outside the context of childhood trauma. To deny those people their identities would be wrong, and I do not believe they are "diverting resources away from people who 'really' have DID or making DID look bad". The ones making DID look bad are the ableists, not people with the disorder. Additionally, the identity of a person/identities of a system is/are always in flux and is/are unique to that person/that system, so I refuse to hate endogenous systems.
Moving on, I notice that people who do not have DID are quick to slap the DID label on Link only post-adventure, claiming that the Four Sword can somehow cause DID and refusing to do proper research on how DID manifests outside of the popular perception of it (i.e. horror movies or Sanders Sides). Certainly, a portion of the Four Swords manga fanbase which has the disorder sees itself in Link and what happens to him, even during canon when he is still split. These people are the ones I trust more to make a call on whether Link has DID or something similar to it. They also seem to consider more parts of the disorder other than just the fact that the system exists and different alters front from time-to-time. In my mind, the readings of Link as having some kind of dissociative and/or identitiy disorder made by fans who themselves have these disorders are much more valuable and plausible. These depictions also seem to be favored more by those individuals than the ones I mentioned earlier, which focus only on the "identity" part of the disorder and none of the "dissociative" parts, leading to an almost flanderized version of the disorder.
Regardless, I wrote this entire preface to say that I am not trying to write Link as having DID post-adventure, and I will disclose now that I am not plural. My goal here is to share what I believe the result of having his soul split would be. If it happens to sound similar to DID or other dissociative disorders, well, I love to headcanon that he has them, but they manifested prior to the adventure and are only exacerbated by what happened afterward. After all, I firmly believe Vio dissociates at least one time in canon, and I could even argue for Green, Red, and Blue dissociating at some point as well, so Link has to have already had dissociative issues in the past.
Moving on, what is "the Brain Fuckery"? The Brain Fuckery is my humorous name for my headcanon encompassing everything that changes in Link's mental state after becoming one being again at the end of the manga. WIP FOR NOW, SPENT WAY TOO MUCH TIME ON THE COMPUTER TODAY.