There are two references in the Bible to the pool of Gibeon. The first is in the account of a conflict between Abner and those aligned with King Saul, and Joab and the servants of David (2 Samuel).
Abner the son of Ner, and the servants of Ish-bosheth the son of Saul, went out from Mahanaim to Gibeon. And Joab the son of Zeruiah and the servants of David went out and met them at the pool of Gibeon. And they sat down, the one on the one side of the pool, and the other on the other side of the pool. (2 Samuel 2:12-13 ESV)
Arnold’s entry in The Anchor Yale Bible Dictionary says,
This “pool” undoubtedly refers to the impressive water system uncovered at el-Jib during recent archaeological excavations” [by Pritchard in the 1950s].
The pool had been constructed in the late 12th or early 13th century B.C. At first, it was thought to be a reservoir intended to hold water. Later it was learned that it served as a stairway leading to a source of water underneath the city.
After the destruction of Jerusalem by the Babylonians, the king of Babylon made Gedaliah governor over the land. A rebellion led by a man named Ishmael killed Gedaliah at Mizpah (Jeremiah 41). The followers of Gedaliah and the men of Ishmael met at the great pool in Gibeon.
they took all their men and went to fight against Ishmael the son of Nethaniah. They came upon him at the great pool that is in Gibeon. (Jeremiah 41:12 ESV)
For more information see James B. Pritchard’s Gibeon Where the Sun Stood Still (1962). For a ground level photo of the pool, see here.