Some of them did. The Classic Maya recorded eclipses and other lunar events in a book that we have named the Dresden Codex. Within the Dresden Codex are 69 columns of bars and dots representing numerals along with calendrical and noncalendrical glyphs. These dates span a period of 11,959 days. Within these dates are lunar and solar eclipse dates which have been checked against other recorded eclipses and are genuine.

The paper Classic Maya Prediction of Solar Eclipses by Bricker et al. (1983) goes into a tremendous amount of detail on how the calendar works, how it correlates with Western calendars, and how it records and predicts eclipses. I have linked it to you through Dropbox if you'd like to read it yourself.

A solar eclipse is central to the debate about when exactly the Haudenosaunee (Iroquois League) was founded. During the council in which the main proponents of the confederacy were trying convince the Seneca to join, a solar eclipse occurred. This encouraged some of the more reluctant Seneca councilors to join the confederacy and since they were the last national-level holdouts this is regarded as the day the Haudenosaunee itself was founded. A few more things had to happen before the league was fully up and running, but at least all Five Nations had agreed that it should exist.

When this was first examined by Euroamerican historians using 19th Century astronomical data, the available solar eclipse tables only went back a few centuries. A good match wasn't found. There were partial solar eclipses at the time that would have been visible from western New York, but none of these were the dramatic total solar eclipse described in the oral histories.

Employing more modern NASA-derived solar eclipse tables, a more fitting eclipse was found. The center of the shadow passed very close to where the Seneca council convened and would have occurred a couple hours after midday and lasted four minutes (about 3:20-3:24PM), making it a great candidate for dramatically interrupting the Seneca deliberations after already considerable debate. Assuming this is the eclipse, then the Haudenosaunee was founded on August 31st, 1142.

Barbara Alice Mann and Jerry L. Fields's paper "A Sign in the Sky: Dating the League of the Haudenosaunee" has more information about this and the debate around it. If you can't access it there, this website also has it.