Thank you everyone for your thoughtful comments and ideas, I want to share the current working hypothesis.
A Houston roofing and construction firm came out to inspect the house. Not shown in the photograph is the continuation of the cathedral ceiling to an outdoor patio. Twenty feet to cathedral ceiling is indoors and extends an additional 10 feet outdoors. The entire length of the cathedral ceiling has soffit vents on both sides. When the roofer replaced the roof 2.5 years ago, they did not reinstall the last 20 feet of ridge vent, over the outdoor patio and 10 feet into the living room. As a result, trapped humid air migrates to the remaining 10 feet of ridge vent over the living room and contacts the cool ceiling and surfaces inside the house enabling mold to grow.
The appearance of inside mold seems to be consistent with the missing ridge vent on the roof. Using Google earth, (thank you BadAir), we were able to confirm the existence of ridge vent on the original roof.
This is still working hypothesis but it seems to make sense.
Jim, I’m going to install the gutters for good measure.
Marc, I mounted a temperature and humidity meter at the peak of the cathedral ceiling. The air is 7 degrees warmer at ~45% humidity. We are experiencing dryer than normal ambient conditions currently so I want to keep this test going. Once I have a baseline, I will reverse the ceiling fan direction for comparison.
JamesPW