En-shemesh

Fountain of the sun a spring which formed one of the landmarks on the boundary between Judah and Benjamin (Josh. 15:7; 18:17). It was between the “ascent of Adummim” and the spring of En-rogel, and hence was on the east of Jerusalem and of the Mount of Olives. It is the modern ‘Ain-Haud i.e., the “well of the apostles” about a mile east of Bethany, the only spring on the road to Jericho. The sun shines on it the whole day long.

en-she'-mesh (`en shemesh, "spring of the sun"):

An important landmark on the boundary line between Judah and Benjamin (Jos 15:7; 18:17).

The little spring `Ain el chand, East of Bethany, the last spring on the road descending to Jericho, seems to suit the conditions. `Ain el chaud is usually called the "Apostles' Fountain" by Christians, on account of a tradition dating from the 15th century that the apostles drank there.