Unpredictable Roof Leak

Our friends cottage has developed a leak in the shingle roof of the screened porch part of their cottage. The leak isn't heavy, and is less likely to occur during a rainstorm but rather at off rain times. e.g. seems to happen each morning. The roof construction is un- insulated/exposed in this portion of the house. I look up and saw a 16" wide x 6" patch of damp plywood sheathing centered on one of the rafters.
The shingles are old but not curling. This is the only leak and it's not a heavy one. One thing I noticed is that they get a heavy dew build-up in the night time. I wasn't sure if that might be more consistent with the leak.
I didn't get on the roof to check it but might be going back in September when I will try to check it.
Any suggestions?
Thankyou in advance.

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