Good spot on the left corner, however it’s not quite staining the roof tiles at all - just above the tiles.
I had to Google “leeward” to find out what it meant :). I’m not sure about the winds, but I’ve attached a satellite image to show you North and South facing.
Interestingly, there is an identical (same blueprint, same age, same structure) house in close proximity facing the same directions and there are no issues on that corresponding chimney. I’ve highlighted in the picture the two roof top views. I would have thought birds would have found the same chimney location on a different house just as appealing
Seems specific to this one chimney area, on one side of the roof.
Thank you for your engagement on this by the way - I’m finding this useful just bouncing ideas off someone who knows about this stuff.