Outside first
Look at the gutter, downpipe joints, roof edge and any chimney or wall abutment above the stain. A gutter overflowing behind the fascia can wet the wall without a single broken tile.
Does it follow rain?
A mark that darkens after rainfall behaves differently from condensation. Keep a note for a week or two if the cause is not obvious. Weather timing is useful evidence.
Cold corners indoors
Mould in an upper corner, especially behind furniture or on an outside wall, may be condensation. It tends to be more diffuse than a fresh leak stain and may be worst in cold weather even without rain.
Loft clues
Where access is safe, the loft can show wet rafters, staining on underlay or a completely dry roof space. That can save a lot of guessing.