I live alone and actually have people near me quite seldom, in the context of any 24-hour period, and so I don't suppose it's possible to claim separation anxiety in any real sense. I have long struggled with the opposite problem and had no attachments (or at least no healthy ones) to anyone for my entire life, until fairly recently I suppose.
Thesedays I am still learning how it feels to feel fondness, let alone attachment, to anyone, and so am still coming to learn what constitues simply missing someone, versus anything more extreme.
I rather cynically told someone I was experiencing separation anxiety from my T who is currently away, and while I know it isn't correct in the clinical sense, I do feel very anxious, isolated and depressed that he is away so long.
I tend to find that my anxiety surrounding the absence of people is more of the safety net concept than in terms of their actual physical presence. I feel most secure when I know that key people are close by, available and accessible if I need them. That way, I am actually less likely to need them than when I know they are not close by, available or accessible, in which case my anxiety does tend to escalate and increase the likelihood that I will feelI need them.
I doubt there's a category of response that is strange and complicated enough to fit me...
Maddog