It's strange that the island being disputed is called, Brazilian Island as the name makes it sound like there's no dispute at all. Information on the roots of the dispute are scarce. The island is at the confluence of the Quarai, Cuareim, and Invernada rivers. The rivers form a tripoint border with Argentina but the Argentinian border is not under dispute.
In an essay titled, "Islands in Between", Godfrey Baldacchino offers the following observation, "We should not be surprised: borders, in spite of conventional wisdom and official intent, are often porous, permeable features: they are liminal spaces with osmotic properties, important tools in a contemporary game of economic prosperity, military strategy or national security. Even here, islands ‘in between’can play a key role."
The same article quotes the Former Prime Minister of Trinidad and Tobago as saying that his country operates in a state of "betweenity" having been claimed by more than one nation. I like that word. It would have been a good way to describe my career on more than one occasion.