It sounds like one complexity is that while eclipses can be run accurately (maybe not where they are visible), the problem is that when the day occurred is not, and you want to know the day. Apparently, there are some unknown factors affecting the rate of Earth’s rotation a bit, and the error is enough that it becomes significant across millennia.

https://theconversation.com/archeoastronomy-uses-the-rare-times-and-places-of-previous-total-solar-eclipses-to-help-us-measure-history-222709

Changing predictions

Precisely predicting future eclipses, or plotting the paths of historical eclipses, requires knowing the positions of the sun, moon and Earth. Computers can track the motions of each, but the challenge here is that these motions are not constant. As the moon causes tides in Earth’s oceans, the process also causes the moon to slowly drift away from the Earth and the length of day on Earth to slowly increase.

Essentially, the length of a day on Earth is getting longer by roughly 18 microseconds every year, or one second every 55,000 years. After hundreds or thousands of years, that fraction of a second per day adds up to several hours.

The change in Earth’s day also affects dating historical eclipses — if the difference in the length of day is not corrected for, calculations may be inaccurate by thousands of kilometers. As such, when using eclipses to date historical events a correction must be applied; uncertainties in the correction can make ancient eclipse identifications harder to pin down in the absence of additional information to help narrow down the possibilities.

Measuring changing day-lengths

For those solar eclipses that are well established, they open a window into tracking Earth’s length-of-day across the centuries. By timing eclipses over the last 2,000 years, researchers have mapped out the length of Earth’s day over that same span. The value of 18 microseconds per year is an average, but sometimes the Earth slows down a bit more and sometimes a bit less.

Tides alone can’t explain this pattern — there is something more going on between the moon and the Earth, and the cause is still unknown. This mystery, however, can be explored thanks to solar eclipses.

We can measure a change in length of a day on Earth with instruments now, but we wouldn’t be able to capture that change hundreds or thousands of years back in time without a precise measuring stick and records of eclipses over millennia and across the world. Total solar eclipses allow us to peer into not only our own history, but the history of the Earth itself.

So if you had an event that was recorded happening in conjunction with an eclipse, we could maybe tell you pretty precisely how long ago it was in units of seconds. But we wouldn’t know how many days ago it was, because the day is not a fixed unit of time and we don’t know sufficiently-accurately how the length of a day has changed over that period.