You really have no clue, but since you never served it does not surprise me
Irrelevant. Same rules apply whether you are military stationed abroad or on business or just tourists. You drop 'em, you go to the embassy or consulate and register 'em. Otherwise, when they turn 95, they may be inconvenienced and have to get their senator's help with the paperwork.
But my real point is to mock the whacked out legal theories of you birfers, who claim they're ineligible because they were born abroad!