My dad is a twin, his older sister is a twin, my cousings (several sets) are twins. Some of them embrace the idea and do everything together and won't go anywhere without the other one, some want nothing to do with being a twin and try very hard to be seperate from their sibling. My younger cousins (and their older sister actually) dress alike all the time. If they don't wear the exact same thing they have a common color, or a common style. A set of my second cousins are identical twins, and spent the first 15 years of their lives being confused with the other one, so they go out of their way to not be alike now. They don't listen to the same kind of music, they don't talk to the same people. Even though they get along and really care about each other, they hate being treated like one of a set.

My suggestion was for a random like/dislike, not something for every twin to have. Just something else to add a little "flavor" to the game.