Welcome to EH.net. I'm probably the least qualified person to answer your question but it looks like you're new here and I didn't want to leave you with the impression we aren't a helpful bunch here.
This is only what I've heard so take it with a pound of salt. First, getting a security clearance is a big expense for a company and unless they really, really want you, it's unlikely you'll get one. It seems most of those overseas jobs go to former military people that already have the clearance and overseas experience.
I believe there is a website (was it usajobs.com?) that specializes in that type of stuff. Also try Halliburton, Bechtel, etc. An hour or two of google searching should provide some good answers. I seem to remember it was 6 months tours/ 1 month off. From what I've seen posted, the qualifications are very specific, working in technologies I've never heard of.
Now that I've probably discouraged you (sorry), good luck with the job search.
ISC2 Associate, WCNA, CWNA, OSCP, Network+