The Stain Is Rarely Under the Hole
Water runs along the decking and the framing before it drops, so a ceiling stain can be several feet from where the water actually gets in. That is why chasing a leak from inside the house so often fails.
Things worth looking for: a stain that grows after rain, damp or musty insulation in the attic, daylight visible through the decking, and shingle granules collecting in the gutters.
From the air the cause is usually visible. Cracked pipe boots are the single most common leak we find, and they are easy to miss from the ground.
If you would rather just have someone look, the drone inspection is free and you keep the photographs.