I finally decided to deal with what I'm convinced is at least partly mold. My idea is that the dust from the top of the wall washes down in the rain and sticks to porous paint. The constant summer time moisture then turns it to mold.
All flat paint may not be as porous as the next but I've used a number of brands and qualities of paint and most of them watered to some degree or another. The inside of this one meter wall on the roof is stained the same way all around which makes me think I used the same paint. None of the house outside walls have this stain .... so maybe paint quality.
My treatment, which I think it needed, was to scrub twice with a brush, spray pure cloro the next day and then paint it with undiluted exterior semi-gloss. The new paint is actually shiny so I assume less will stick to it or absorb into it. The catch is I'm finding out what a real good paint job costs because this paint is expensive. Still much of the house that never gets wet so I don't have to paint it all at once.
After scrubbing and cloro on one section
Whole wall section painted on top and sides