What type of a connector is this?
Mezzanine connector or board-to-board connector appears to be the term used. Thanks to Dave Tweed in the comments.

http://www.mouser.com/ds/2/185/DF12_catalog-938983.pdf should work I think.

After a lot more googling, I also found a set of technical drawings that describe the use of all of the pins (not posting a direct link as I suspect that it really shouldn't be publicly available, but googling "jbtb1 connector" brings it up)

That document has the mark ACES_88079-0800A1, which lead me to this datasheet for the female connector http://www.datasheets360.com/part/detail/88079-0800a1/-5694048818178298435/