I've always wanted to find a bunch of people to do pedigree studies with regarding personality type. Of course it wouldn't really be legit, but it'd a fun little experiment to do. It would require subjects who are certain (within the possible realms of certainty regarding this topic, that is) of their MBTI type, are certain of their parents' types, and certain of their grandparents and/or aunt/uncle types. By looking at this, you could attempt to hypothesize over which functions are X-linked or autosomal, which are dominant/recessive/codominant, if there's any pleiotropy, etc.
The pedigree would have to be pretty expansive for it to ever mean anything (even something silly). Just knowing your type, your siblings' types, and your parents' types doesn't really get you anywhere. Again, it would be totally silly, but it might be fun. I think most of us would agree that personality has a lot more to do with upbringing and environment than it does with DNA. Though I'm tempted to say that if any functions were genetically linked, it would be the N/S ones.