That’s a good point about the moon. It would also explain why they had both east and west observation points - a full moon rises at sunset, and sets at sunrise, and a new moon does the opposite.
Yep, I can imagine they also followed the planets and their favorite constellations. So one can get pretty accurate with just careful observation of several natural factors combined. But as you mention, once documented this can then progresses into more complicated math and formulas that can be shared as a standard. And we know it did, The later South American cultures were highly skilled at working with complicated math and formulas.
But I would like to share an observation displayed in this thread, and it happens all the time and is common. For some reason we tend to try to theorize and search for that one influence and factor to explain these things. When in reality it could actually be several factors in combination, or there could even be an unseen lost variable we will never find. I have to be honest and admit I sometimes get caught up in that frame of mind myself and have to back up, regroup, and look at it again for other variables I had not considered.
And it is natural, we just tend to do that. Take for example these towers and their alignments. These have probably been looked at and researched for years now but no provable connection was made with the solar solstices and equinoxes until they adjusted the current alignments to what they actually would have been back then, because back then the earth’s axis was totally different from now.
So until they threw it into a computer model and reversed the clock back to what the alignments actually were back when they were built, they didn’t align with anything and made no sense. That was the unconsidered factor and variable until someone decided to take that into account. Then it all fell into place and they aligned correctly. :)