Ryan Akagi has BPD
✪ Ryan repeatedly tries to avoid abandonment/rejection, at times doing really reckless/impulsive things to keep this from happening in his personal relationships (this doesn't really work). He engages in reckless, sometimes life-threathening behavior in general
In "The Twin Tapes," it is shown that Ryan has dated at least three people within less than a year, even giving his van to his last ex-girlfriend in a last-ditch attempt to save their relationship. All three relationships can be inferred to be short lived, at times unstable. Like all the others, his last girlfriend ends up breaking up with him. As much as he pretends other wise, Ryan doesn't enjoy the idea of "going solo" or being alone in general.
In the same episode, Ryan shows up at Min-Gi's place of work, trying to convince him to tour with him like they planned with a show in New York (which may or may not have been true on Ryan's end). When that fails, Ryan ends up stealing Min-Gi's work keys to bait him into following along.
Outside of his relationship drama, Ryan has been shown to act on impulse. One notable instance is when he ran through the various doors in the Astro Queue car and nearly stumbled off of a cliff and fell to his death (The Astro Queue Car)
✪ Ryan displays a lack of "self" or "identity"
This is a bit of a reach on my end but in "The Twin Tapes" Ryan is shown repeatedly and drastically altering his appearance during the "split screen" montage, suggesting that Ryan himself has a hard time figuring out who "Ryan" is and what that means for him.
✪ Ryan is prone to intense/inappropriate moments of anger
(Off the top of my head)
Hitting his fist on the table and raising his voice at Min ("The Twin Tapes"), interrupting Kez by hitting the wall/door ("The Iceberg Car"), snapping at Min-Gi in the astro queue car ("The Astro-Queue Car")[although I will acknowledge Min-Gi provoked him quite a bit in this episode], shifting from laughing along with Min-Gi to calling him "dead weight" within the same episode (this can also be read splitting, a symptom of bpd), knocking a vase to the ground and smashing it in a sudden burst of anger, his argument with Min-Gi ("The Art Gallery Car"), snapping at Kez ("The Castle Car")
These are less extreme, but Ryan has other moments of growing hostile or irritable with either Kez or Min-Gi. Examples of this include" brushing Min-Gi off when questioned about his sarcastic remarks toward Min-Gi going to uni (I believe this was the Iceberg Car?), assuming Kez left the two to get executed (The Old West Car), his response to Kez revealing that she melted all the butter(the Pig Baby Car), in general Ryan is more likely than Min-Gi to become frustrated with Kez's antics [sometimes assuming the worst], after he's booed off the stage a SECOND time he angrily tells Min-Gi they're leaving and attempts to yank open the train car door before confronting Min-Gi (The Party Car)
✪ Min-Gi is Ryan's favorite person
It can be argued that Min-Gi is the most important person in Ryan's life and that most if not all of Ryan's happiness revolves around his best friend and bandmate, considering how he's notably miserable without him while going solo, even when in a room full of other people. I wouldn't go as far as to say that he idolizes Min-Gi, but he definitely holds Min-Gi up to high regard, and is ultimately crushed when Min-Gi leaves him the first time, and again when he has to relive being left alone on stage in the Party Car. The first time this happens, Ryan is pushed to leave Powell Lake and go solo. The second time, Ryan is more visibly angered and tries to leave the Party Car. (At least this time he doesn't leave without Min-Gi)
I will also note here that it is repeatedly implied that Ryan does not feel his parents care about him/his feelings unless he does something to get their attention (likely acting out or putting on a "persona" of confidence). Ergo, he becomes attached to Min-Gi in response.
✪ Ryan experiences dissociative symptoms during times of high stress
Ryan is notably 'not here' mentally in "The Mega Maze Car", and would've gotten crushed by Pig Baby's arm had Min-Gi not pulled him out of the way in time. For context, this scene takes place right after Ryan and Min-Gi have a heart to heart and Min-Gi admits that he doesn't trust Ryan (which is understandable, but probably devastating to hear from your best friend, especially while you guys are supposed to avoid angry and homicidal train denizens)[and also feeling immense guilt for almost leaving Min to die when he got his exit]{so essentially Ryan's got a lot going on in his mind at the moment}
✪ Ryan displays suicidal and/or self-destructive behavior
Everyone is open to their own interpretations of this scene in "The Train to Nowhere" but between Ryan completely shutting down, refusing to eat or talk to anyone, coupled with the fact that his number has not made significant progress AND the fact that Min-Gi distrusts him (rightfully so, but Min-Gi doesn't know that), AND they are trapped inside a living castle with a grudge, it's not too much of a stretch to infer he's at his wits' end here and is resolved to die in this castle.
Not a critera persay but impulsive behavior is typically associated with bpd (although being impulsive does not inherently mean you have bpd on its own, jsyk), which *gesturing to Ryan in general* he's got it.