Extraverted Sensing (Se): Captain Jack lives spontaneously in the moment. His default strategy is improvisation, and relies on awareness of the physical environment and manipulating other people’s emotions (tertiary Fe) to get what he wants. He’s always paying attention to immediate opportunities and takes advantage of the most obvious solutions rather than trying to strategically figure out the best solution. He’s a very physical person, interested in one-night stands and relationships based primarily off of the physical, though he is clearly capable of much deeper types of love. He loves action and rarely gets scared in stressful situations. Jack doesn’t think much about the past, to the point of forgetting many of the major events of his childhood.
Introverted Thinking (Ti): Jack is a problem solver, but he doesn’t necessarily think through all of his decisions before he acts. He comes to fast, rational solutions that usually work. He is honest, though not necessarily direct, and doesn’t base his logic off of empirical evidence. He makes his decisions based on an internal logic (what makes sense to him) rather than considering facts. He would rather make a rational choice and suffer for it than make an irrational one and get off happy.
Extraverted Feeling (Fe): Jack has an all encompassing love for those he is close to, and despite his cold nature, is able to show love and compassion for them when they most need it. Jack’s moral philosophy hinges on the phrase “an injury to one is an injury to all.” He willingly (albeit painfully) sacrifice his own grandson to save millions of other children. He’s incredibly aware of other people’s feelings, often noticing what other people fail to see about themselves. He often uses this understanding to manipulate people through charm and flattery.
Introverted Intuition (Ni): Jack is witty, but is not necessarily an idea person. When under stress, he doesn’t think of multiple solutions: he thinks of the most direct and obvious solution (Se dom, Ni inferior). This is the least developed of his functions, and doesn’t really develop until he’s been with Torchwood for decades. As the face of Boe, he plays with the Doctor’s mind a bit, dropping hints. Over time, Jack gets better and better at predicting the future, so that he’s able to know when his Torchwood team is making a huge mistake, but not usually in time to stop them.
I’ve also seen Jack Harkness typed as ESFJ and ESFP, but I think these are both based on slut stereotypes and a lack of exposure to Torchwood. He’s not an Fe dom, and he doesn’t use Fi. However, he is an Se dom. In Torchwood, you get to see Jack’s development and life in much greater depth than in Doctor Who.