Great article by Prof. Peter Beck of Keio University of the benefit of the potential Korea-Japan alliance, and what Japan needs to do to make it happen:
While Tokyo continues to claim Dok-do, the average Japanese just doesn’t care. Most Japanese would not be able to find the island on a map. Indeed, I could not find a single public sign in Tokyo or any other of the seven major cities I have visited concerning ‘Takeshima’. ...

I told my Japanese audiences that if Tokyo renounced its hopeless claim, there would be a flood of Korean goodwill. Yet, many Japanese believe this would undermine Tokyo’s claim to the Northern Territories (even though Moscow shows no intention of even discussing what it calls the Kurile Islands). Keio University’s Soeya Yoshihide argues that the real issue is Japan’s domestic politics: the right-wingers must be placated. Japanese are crazy about Korean food, dramas and Girls’ Generation, not Dok-do! Given Korea’s military control of Dok-do, Tokyo’s claim should be ignored.
A Korea-Japan alliance? [East Asia Forum]

Parts of the article sounds awfully like the Korean's idea of a potential Godfather offer that Japan can make to instantly improve its relations with Korea. The Korean can't help but think he might be in the wrong gig.