This question makes no sense as stated.
a) There is a huge difference between solar and lunar eclipses in this respect.
(Lunar eclipses occur everywhere, while Solar eclipses only on a small area on the Earth). For this reason, a solar eclipse is much harder to predict for a given location.
b) The accuracy of prediction improved slowly with the development of astronomy.
So "Predict accurately" needs much further specification.
c) Predict how much in advance?
d) Most solar eclipses are incomplete: only a part of the Sun is obscured. This can be a very small part on a given location.
Prediction of Lunar eclipses was possible already with Babylonian astronomy. Reliable prediction of solar eclipses for a given location few years in advance became possible only in the middle of 18th century when Lunar theory was fully developed. But there are reliably recorded cases when a lunar eclipse was predicted using ancient Babylonian methods. These cases happened in 18s and 19s century when predictions were made by Tamil (in India) astronomers using Babylonian methods, and recorded by French and English travelers.
But one cannot predict a solar eclipse reliably (for a given location) with these methods for the reasons I explained above.
By the way, Kepler laws have little to do with the problem. For the Moon, Kepler laws give only a crude approximation, comparable in accuracy to what Ptolemy already knew. The reason is that the system Earth-Moon-Sun is a three body problem, while Kepler's law is a solution of a two body problem.
It is good for planets. But gives a very rough approximation for the Moon.
Good theory of the Moon motion (sufficient for reliable solar eclipse prediction) was developed only in the middle of 18th century.