Animals are fearful of lightening and thunder, as harbingers of trouble. Do animals see rainbows? Animals react to environmental changes, and there is probably a lore about animal behavior during eclipses. I expect there is no evidence of other animals forecasting eclipses.
Very early humans probably treated total solar eclipses as they treated storms. They adapted. Later, in advanced tribal times with social structure and shamans, the total solar eclipse became significant. Are there ancient artwork of eclipses or even moon phases? What records do we have of early shamans and eclipses? The role of shamans in human history is very significant, but I won’t go into it here.
Shamans and tribal culture could elevate eclipses to significant religious events. When shamans could predict solar eclipses with some accuracy they could command much more respect. I have read (but have no reference here) that total solar eclipses could have been forecast in tribal times from basic stellar and moon data. The lack of total accuracy was actually advantageous for the shaman. He would have the tribe perform rituals to keep the eclipse away (the moon eating the sun); if the prediction failed and there was no eclipse, the ritual was successful. If the ritual failed, more ritual during the eclipse would assist the shaman in bring back the sun. Failure of tribal persons to properly perform the ritual would be cited for the reason the eclipse happened.
Although total solar eclipses are rather frequent for somewhere on Earth, they are far less frequent at any specific location: about one every other generation. Total solar eclipses would be in the lore of a culture, not a periodic occurrence. Partial eclipses would have been more frequent.
Being able to predict solar eclipses motivated some tribal persons, especially shamans, to attend to the details of the night sky, which launched humankind on it path towards sci/tech civilizations. Seeing constellations in daytime that were seen only in other seasons at night, was probably a significant feature.