Eclipses were often considered to be portents of disaster, however, we are not concerned with such superstitious ideas. However, some records of ancient eclipses have been sufficiently detailed to enable them to be used as chronological anchors. Stavros Papamarinopoulos has used such records to date the Trojan War(d). A 2012 paper by Göran Henriksson also used eclipse data to date that war(e).
Encyclopedia Britannica notes(b) that “well over 1,000 individual eclipse records are extant from various parts of the ancient and medieval world. Most known ancient observations of these phenomena originate from only three countries: China, Babylonia, and Greece. No eclipse records appear to have survived from ancient Egypt or India, for example. Whereas virtually all Babylonian accounts are confined to astronomical treatises, those from China and Greece are found in historical and literary works as well. However, the earliest reliable observation is from Ugarit of a total solar eclipse that happened on March 3, 1223, BCE. The first Assyrian record dates from much later, June 15, 763 BCE. From then on, numerous Babylonian and Chinese observations are preserved.”
On the other hand evidence of eclipse prediction does not go back as far, although in the 1960s when the 56 Aubrey Holes at Stonehenge were interpreted as functioning as an eclipse predictor by astronomers Gerald Hawkins and Sir Fred Hoyle, and by amateur enthusiast C.A. `Peter’ Newham, it brought an outcry from the archaeological community.
In 2015, William S. Downey published a paper with the intriguing title of ‘The Cretan middle bronze age ‘Minoan Kernos’ was designed to predict a total solar eclipse and to facilitate a magnetic compass’(a).
The Phaistos Disk, also from Crete has been described as an eclipse predictor as well(c), but this is just one of the many and widely varied theories.
In my opinion, the object we have with the greatest potential as a predictor is the Antikythera Mechanism, dating to around 200 BC. However, nothing so far can be definitively proven as an eclipse predictor.
(a) (PDF) The Cretan middle bronze age ‘Minoan Kernos’ was designed to predict a total solar eclipse and to facilitate a magnetic compass (researchgate.net)
(c) (99+) Counting lunar eclipses using the Phaistos Disk | Richard Heath – Academia.edu