In the article penned by Rami Khouri, Where John Baptised, published in the book “Exploring Jordan: the Other Biblical Land” (BAR, 2008), the archaeologist journalist cites the data conforming the location of the baptism site on the eastern bank of Jordan. In both cases, when this location is mentioned in the Gospel of John (1:26-28 and 10:40), we encounter visitors from Jerusalem. Facing from the “holy city”, the site is indeed beyond the Jordan. On this spot, along the Wadi el-Khurra, Helena, the mother empress of the Roman Empire set up the church of St. John the Baptist in the early IV century CE. Later, here rose a monastery complex containing several churches, the caravanserai to accomodate pilgrims on their way to Mount Nebo, and a cave of John the Baptist.
The alternative site is depicted on the Madaba map of the VI centiry CE where it is placed on the western side of the Jordan. The legend runs that it is Beth Abara (Hebrew: “House of Crossing”), “the place of the baptism of St. John.” The artist was likely facing the site from Madaba and might misunderstood the meaning of “beyond the Jordan”.
The further research, in my view, should be devoted to the bedrock of the Jordan. The author refers to the fact that the river shifted its course many times and that until the mid-20th century it would expand, when flooded, to nearly a mile in width. The bare statement is not covered by the data necessary for the evaluation of this statement. The counter argument says that both sites could function in different times according to the shift of the river. A new challenge for explorers.