Fwiw, my own experience/impressions:

1) I too have the pink rash. My GD started with itchiness and a few bumps on my face, which a doc diagnosed as rosacea. It progressed to my neck, which looks more like the pink rash you describe, then to my shoulders, back – where it was diagnosed as GD based on a punch biopsy – and also went to my chest, where it started out looking like the GD but at some point really seemed more like the pink rash. Then it went to my armpits, and it's currently bothering me most in my inner elbows – in both those places, it's the pink rash.
By pink rash, I mean something that may not have the larger bumps I got with GD but extremely itchy, often very bright pink especially in the folds of skin, often with smaller bumps. The bumps I'm calling GD may be pink, but they're not necessarily surrounded by pink, inflamed-looking skin; they're sort of more isolated, like a mosquito bite.
gardeningjunkie suggested the pink rash is atopic dermatitis, and it does look like the photos of that disorder. My doc never mentioned any separate diagnosis for it, although I don't think he thinks it's GD, since it prompted him to test me for allergies.
All of it seems to have developed in a slow but steady progression downward from my eyebrows; my own thought is that the two kinds of rash are connected but manifest differently in different types of skin – the GD in areas where the skin is thicker and tougher, the pink rash in areas where the skin is more tender and moist – but I've never seen or heard anyone else express that theory. No treatment of any of it has done much for me, except for varieties of cortisone cream, which does have the hazard of thinning the skin, so it's been kind of an awful balancing act.

2) Demodex are a suspected factor in GD, and my problems started while staying in the least-clean BnB I've ever stayed in. I've wondered whether there's a particularly virulent strain of the bug, but at this point I've tried everything to get rid of/control them and have to conclude they're either gone or immortal. I've seen occasional other stories, though, of people seeming to catch GD from a mate, and wondered if demodex could have something to do with that.
On the other hand, it also seems to me that a lot of people develop these kinds of rashes as they get older – one of my parents did – so I'm thinking it may be at least partly a matter of our skin becoming more vulnerable to malfunctions of some kind, so that when similarly-aged mates develop similar problems, it's just because they're similarly-aged.