Well, that took a bit more searching than I thought it would. Apparently the answer is yes, or yes - sort of. I found one site that mentions eccrine sweat glands specifically as part of the eyelid anatomy. Most sites only referred to the specialized glands of Moll or Zeis; I suppose the default assumption is that unless otherwise indicated, there are eccrine glands present. Ergo, they are present in the eyelids. But it's hard to reconcile "sweat glands located deep in the dermis" with how thin the dermis/epidermis is in the eyelid...
Anyway, having established that eyelids can indeed sweat, I can return to wondering why the sensation has only become noticeable post-gbs. Maybe they never needed to work very much when I was heavy, since I had more skin surface area? Or am I just better at paying attention to my body now? Hard to say.