Elthece in tribu Iudae. Est hodieque Thecua vicus in nono ab Aelia miliario contra meridianam plagam, de quo fuit Amos profeta, cuius et sepulcrum ibidem ostenditur.
(Jerome 87:13-15)

Eusebius, Onomasticon 86:12-14 (ca. 295 A.D.); Jerome 87:13-15 (ca. 390 A.D.)
Eltheke (Jos 15:59), in the tribe of Judah. And today there is a village called Thecua, [12 miles] at the ninth milestone from Jerusalem [to the east] to the south, whence was Amos the prophet, whose tomb is shown there to this very day.

BIBLICAL BACKGROUND

Josh 15:21 .59 Places of the tribe of Judah
The towns belonging to the tribe of the people of Judah in the extreme South, toward the boundary of Edom, were...59 Maarath, Beth-anoth, and Eltekon: six towns with their villages.

Amos 1:1 Amos the prophet
The words of Amos, who was among the herdman of Tekoa, which he saw concerning Israel in the days of Uzziah king of Judah, and in the days of Jeroboam the son of Joash king of Israel, two years before the earthquake.

Jer 6:1 Blowing the trumpet in Tekoa
O ye children of Benjamin, gather yourselves to flee out of the midst of Jerusalem, and blow the trumpet in Tekoa, and set up a sign of fire in Beth-haccerem: for evil appeareth out of the north, and great destruction.

MORE ANCIENT SOURCES

Petrus Diaconus, de Locis Sanctis (Appendix to: Egeria, Itinerarium) L2 (12th cent. A.D.)
In Anathoth is the tower where the prophet Jeremiah uttered his Lamentations. It is four miles from Jerusalem. Twelve miles from Jerusalem is the tomb of the holy prophet Amos, at the place called Tekoa.

Cyrillus Scythopolitanus, Vita Sabae 36 (6th cent. A.D.)
The holy Elder observed their grievous state of distress - for they had neither a church nor a chief, but would take Communion on Sundays in the memorial of the holy prophet Amos in Thecoa, and besides, they were plunged in the disorder of anarchy, quarrelling and divided among themselves. (Sabas) pitied them and related their situation to the patriarch, asking him to organise them (in an orderly community).

Willibaldus, Vita 23 (724-726 A.D.)
After praying there [Bethlehem] they went on and arrive at a large village called Tekoa, the place where in old days the children had been murdered by Herod. A church is there now, and there is one of the Prophets buried there.