Good work Tim. But what about NASA Administrator or Postmaster General? Or do they not count as part of the cabinet even unofficially?
These are all official Cabinet and Cabinet-level officers as defined by law and presidential prerogative (with some extrapolating as to who the Presidents might include with Cabinet-level positions).
"Cabinet" officers only refers to the group of 15 (14 here) Secretaries that are confirmed by the Senate and defined explicitly by law. They are in the line of succession.
"Cabinet-level" officers refers to those who, by Executive Order, are put into the Cabinet to advise the President during Cabinet meetings as equivalent to another Department Secretary. Since 1971, the Postmaster General has nothing to do with the President (he or she is appointed by a Board of Governors).
The NASA Administrator, while concurrently the Senior Space Advisor to the President, has never really been involved in Cabinet meetings to my knowledge (maybe in the '60s/'70s?). Alot of Federal agencies are like that (FEMA, FBI), and it really has to do with what a President deals with on a day-to-day basis.