Read this in late 70s from school library, was old book. Paperback in landscape orientation, man looks for clues, crawls through tunnel under lake to island and lighthouse(?). Think it was a ghost?
Stump the Bookseller
New format, same book stumper solving.
You may be thinking of THE HAUNTED SPY by Barbara Ninde Byfield.
https://www.kirkusreviews.com/book-reviews/barbara-ninde-byfield/the-haunted-spy/