Anyone have any idea what book I’m talking about?

I read this book when I was about 14-15 (like 4-5 years ago) and cannot remember the title or author of it for the life of me. This is from my very dodgy memories but I hope it makes sense.

The book starts off with a man going to an island for something (I believe it’s to do research on the locals and their culture or some sort of phenomenon that happens on the island that the locals know about). There he meets a young woman (his age) and they start talking. This all the first-ish chapter.

The chapters then start going back in time (bear with me). Each chapter starts showing a story of a man and a woman on the island, who in is each other, are in love, have a family, or anything like that, and it becomes clear that each chapter is further and further in the past and that the man and woman are something like the previous lives of the man and woman from chapter one. If I remember correctly, in each chapter at least one of them dies or disappears.

On the second to last chapter, and the furthest point back in time, there’s something like a sacrifice (in a more medieval-esque setting) where they both die and promise each other to find each other in each life.

After that, the last chapter returns to the present of the first chapter where the man and the woman start having a connection of sorts and basically fall in love. I think the man decides to stay on the island with the woman, though take that with a massive grain of salt.

That’s like the whole book basically summarised. The whole story in every chapter is confined to that one island and the story or the characters never leave it. There’s only ever references to the outside world (especially in the first chapter about the man’s job or something) but the reader never sees it or experiences it, we never leave the island. Sadly I don’t remember for certain if the book is 1st or 3rd person, but I think it was 3rd.

Anyone have any idea what I’m talking about or am I crazy??