Given that PTWOB-Flyer flew F-15's, I'm thinking he's more interested in the AF side (although the USN/USMC have way more C-12's and better locations by far).
The AF actually only owns a few C-12's. Embassy support C-12s are owned by DISA (Defense Intel Support Agency) and flown by AF pilots (yes, a quibble). You'd have to get the Assistant Air Attache job at one of the handful of embassies that have them.
AF C-12s are at Osan, Elmendorf, and Dahrhan. Osan has the J, aka Beech 1900C. There's 9 pilots, including the unit/CC, a mid to senior Maj. He's on a 2 yr tour, accompanied by family. Everyone else is 1 yr. 2 of those pilots are attached, 1 at 7 AF, 1 at the OSS. They fly about 350 hrs a yr, mainly on Korea and to/from Japan. Everyone is prior heavy AC, so you take an AC check, then fly for a couple months in theater before finalizing upgrade. Sims are located at the Flight Safety facility at LaGuardia, with flying qual done at Elmendorf (see below). It's the 1900C, with appropriate type rating. It looks like a King Air on steroids, but performs like a King Air on qualudes. Slower, lower ceiling, crappy brakes, but hauls 19 pax.
Elmendorf is a 3-yr tour, mostly ex-C-130 guys. They're actually a sub-unit of the C-130 squadron there, with their own DO, but they answer to the 130 CC. Kinda wierd setup. They have 2 of the King Airs, and one J model. They serve as the J model schoolhouse, since Osan's 1-yr tours preclude the continuity necessary for that. Everyone I knew there loved the location and flying.
Disclaimer: I was the DO of the Osan unit in 1999, so some of this might have changed somewhat. Tho I met a guy that just got an Osan assignment, so they're at least still alive & kicking.
Dahrhan (spelling?) is a 1-yr tour, but I think they're down to 3 pilots now. PM me if you need more info, as there's a guy in my unit who got back a yr ago. Standing rumor is they'll be moving to Riyadh, but the MX contractors don't want to go there, so the move is "on hold."