After watching some videos, SLE-Ti is my suggestion.
Here are some miscellaneous observations. I apologize, it's rather chaotic.
What I first noticed was the lack of intuition: Give Logan a challenging (important - he stresses that a couple of times in what I've watched) script that he likes. He'll ace it, period - he started acting at the age of 2. Never did anything else. Actually explaining the underpinnings of plots/characters/temporal allocations/concepts, however, gets Logan into trouble.
All the questions in interviews somehow bother him, he's not in his element. He likes the venue more than the interview, it seems. He repeats himself or the words of the interviewer all the time, stutters, stops often. Yet, he becomes very attentive when somebody gives a rundown of human history or makes some other related statement - Ni DS. Intuitive insights are the #1 way to amuse or carry Logan along. He starts nodding, he giggles, becomes less `larger than life´, frowns and takes up a thinking stance.
Winning a Teen Choice award, his first comment on stage was about the actual trophy. Nothing was rehearsed, he just improvised and kept saying how the love of the fans means a lot to him when people started screaming. Se-Fe, irrational. No expert grasp on abstract ideas - too rooted in the here and now. You can see him glancing around all the time, reality's the most interesting thing to Logan. He likes to make audiences react. Usually engages successfully in games that interview hosts play on their shows. Armed combat seems to be his specialty in movies (Percy Jackson, Three Musketeers, Fury). He's super fast at everything His skills are impressive, but that's just me being biased towards Se. One thing that is striking is his overall choice of roles, it's either action (Se) and/or drama x romance (Fe).
Everybody seems to demand Fi from Logan but he can't quite deal with it. His PoLR slips go like this: "Logan, what would you do if the world ended tomorrow?" The other interviewee says something about spending the day with their family. Logan, on the other hand: "Screw family, I'd go to London and drink Guinness beer." I imagined @Maritsa reacting to that. Here's another occasion: Logan talks about the lead actress. "She's a wonderful person. Which makes work... going to work nice?" Turns to the director laughing awkwardly in order to get approval.
Another one: (On conflict with Brad Pitt and his own approach to acting) "My character in that film was like, basically, you know, he's a nonconformist and I was trying to be, uh, nonconformist throughout the shoot so I'd kind of be a little bit of a jerk while working with him". He says that they became friends later, though, complimenting Brad's persona. Aka: Logan uses Fe to deal out praise (which almost always returns, making him happy) to balance his PoLR.
The general intonation (ExTx business-like) and eyebrow game sealed the deal for me, ESTp. Probably a Ti-subtype.
@Aylen, what does your gut say? Dual potential?