Some people behave rather oddly. The Doctor acts in ways that baffles his companions and throws his opponents off their game, switching from excited schoolboy to dark and imposing in a moment. The Eccentric trait means the character has a behaviour that makes them stand out, or sometimes makes it more difficult when interacting with others. As a Minor Bad trait, their behaviour isn’t too upsetting. It could be an odd mannerism during times of stress, out-of-place reactions to everyday events, or even talking to themselves.
The Major Bad Trait, is probably too unpredictable to be purchased by a player character. We’re getting into seriously wacky territory, sometimes a little dangerous to be around. Missy is a prime example of someone with the Major Eccentric Trait, straying into unpredictable behaviour with little provocation. But just because the character has a Major Eccentric Trait, it doesn’t mean they’re homicidal (except it does in Missy’s case, of course).
The specifics of the character’s Eccentric trait should be discussed with the Gamemaster at character creation. Just how does this behaviour manifest? Are they aloof, a loner, irrational, tangential, a natural clown, a sour-puss? Once their odd behaviour is defined, the Gamemaster will help to decide how this behaviour is triggered. Is it when they’re stressed, cross, happy, jealous, or tired? It is then down to the player to act in character when the situation arises, which will gain them Story Points for good roleplaying.