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There's a thread comparing a possible WWII Japanese invasion of Australia with the planned (and near-universally derided) German plan to invade Britain, Operation Sea Lion. Someone in the thread said a Japanese invasion of Ceylon (modern Sri Lanka) would be more realistic.
(Also, apparently there was a Trotskyist-inspired Ceylonese military mutiny as well as a lot of wartime agitation against the British. This seems like something a hypothetical Japanese invading force could capitalize, although given the Japanese Empire's OTL thuggery, they'd probably lose local support really fast.)
What kind of damage could the Japanese do to British India if they held Ceylon?