The internships I have found so far through resources like the State department and usajobs.gov are all specifically for students. I've also emailed the person in charge of State department internships, asking if she knows of any non-student internships, and she has not heard of any.
Of course, this does not mean there is no cache of non-student internships out there. I simply have not found any through the resources I know of.
It's fairly plausible that most/all government internships are specifically for students, so if you've looked carefully and not found things then they may not exist. However, consider looking for local government; it will probably transfer well, especially if you can find internships with large cities or counties/regions.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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