If the Euphrates here is the Euphrates we assume it is, then I don't think any of the rivers should be looked for in Arabia, or anywhere south/west of the Euphrates. What leads people to look there is an assumption that this Havilah must be the same one that shows up in Arabia elsewhere in The Bible. But there are two Havilahs in Genesis 10, I feel every Arabian Havilah is of Joktan while this Havilah being close to a Cush could be the Havilah of Cush. In fact it could be in this context Havilah and Cush are different names for the same place existing between the Pison and Gihon.
I've talked before about how Cush wasn't only in Africa, I see evidence to link him to India, and I suspect some of the Indian Cushites were initially in Iran for awhile. This Havilah is probably Hoveyleh.
I believe there is significance to the order the rivers are listed in Genesis 2, something most popular theories about them don't consider. Particularly I think it likely they are starting in the East and going Westward. They are listed in the order Pison, Gihon, Hiddekel and lastly the Euphrates. So if that is the Euphrates we assume it is, and the Hiddekel is indeed the Tigres, then the Gihon would be the Karkheheh river and the Pison would be the Karun river, known in classical times as the Pasitigres. Here is a map taken from the Wikipedia page for the Karun.
Thus making the main River of Eden the Shatt al-Arab.
I'm not the first to propose these two rivers, my exact theory was proposed by at least one prior scholar, and another makes my Pison the Gihon. But some want to take one of these while also trying to place the Pison or Gihon in Arabia. And one website dismissed these two rivers by saying they are too small. But the text of Genesis 2 says nothing about their size, it's merely man's imagination that wants to assume all four rivers were as epic and history defining as the Tigris and Euphrates.
Both of these rivers start in the Zargos mountains, which is why previous arguments for one of them being the Gihon tend to be based on saying the land of Cush in this context is the homeland of the Kassites commonly speculated to come from somewhere in the Zargos mountains.
Al-Qurnah is a place on the Shatt al-Arab that locally claims to be where the Garden of Eden was.
The Karkheh river also plays a role in arguing that the land of Aratta from the Sumerian epics about Enmerkar was in the area of Mt Alvand and ancient Ecbatana, modern Hamdan, which in turn factors into B.J. Corbin's theory about where Noah's Ark landed. His theory also involves using information from Jubilees to suggest the area around where the Ark landed was the ancient settlement of Arphaxad, remember the Book of Judith names the king of Ecbatana as Arphaxad which has always confused scholars.
The Karkheh river also plays a role in arguing that the land of Aratta from the Sumerian epics about Enmerkar was in the area of Mt Alvand and ancient Ecbatana, modern Hamdan, which in turn factors into B.J. Corbin's theory about where Noah's Ark landed. His theory also involves using information from Jubilees to suggest the area around where the Ark landed was the ancient settlement of Arphaxad, remember the Book of Judith names the king of Ecbatana as Arphaxad which has always confused scholars.