I don't understand - why is a Round Earther trying to explain FET/Zeteticism to another Round Earther? You'd think you would have left it to someone who actually knows what they're talking about if you cared so much about truth over starting with a premise and saying whatever it takes to confirm it.
That said, eclipses are cyclical. You can predict future eclipses by following the well-known and documented pattern. This is true for both FET and RET.
Not quite. The Mayans were very good at this prediction, but predictions far into the future did get a day or so out. There are slight perturbations that the Mayans did not know about, let alone predict.
In fact, the Brickers found the astronomical calendar dated to the 11th or 12th century accurately predicted a solar eclipse to within a day in 1991, centuries after the Mayan civilization had ended.
From Ancient Maya Predicted 1991 Solar Eclipse
That is an amazing prediction, even so.
Dates can usually be predicted a reasonable time ahead "by following the well-known and documented pattern", but the details of exactly where they will occur is not so easy. Quite a number of Chinese astrologers ended up headless as a result.
But, if you have some better information, it would be very helpful.