After rain
If the patch darkens after wet weather, the external chimney and its roof junction move up the list. Flashings, soakers, flaunching and open joints should be checked.
Unused chimneys behave differently
Closing a fireplace changes airflow through the flue. If ventilation is poor, moisture can condense inside and salts in old soot can attract moisture. That can produce staining even when the roof is watertight.
One side only
Damp concentrated on one side of the breast can sometimes line up with the weather side or a particular roof junction. That is useful when deciding where to inspect first.
Do not seal everything blindly
Coating internal plaster or external masonry before understanding the source can hide symptoms for a while. The route of moisture still needs dealing with.
