To understand what's going on for the Haudenosaunee (Iroquois), we have to take a few steps back in the Creation mythos.

Sky Woman fell to earth while pregnant and gave birth to daughter named Lynx, who in turn died while giving birth to twin boys. After her death, Lynx became the spirit of the earth. Sky Woman raised her grandsons until her own death, at which point she became Grandmother Moon and continued to watch over her great-grandchildren, humanity. In some versions of the Creation, Sky Woman and Lynx are merged into one character, but since Iroquoian metaphysics gives people two 'souls' (one that travels skyward after death and one that wanders the earth), Sky Woman can be both Mother Earth and Grandmother Moon without any problem.

When the moon reddened or darkened during an eclipse, it meant that Grandmother Moon was either displeased or ill. She needed to be appeased or healed. Unfortunately, my source doesn't give any examples of how Grandmother Moon was appeased or healed. Dances seems to be the most likely method, as the spirits love to see people dancing and dances were often used as community activities in association with healing. Dances could also be organized and carried out within the span of an eclipse.

Sources:

The League of the Iroquois, Lewis Henry Morgan

Iroquoian Women: The Gantowisas, Barbara Alice Mann

This is one of those questions that might have more luck over at /r/askanthropology

Pre-literate cultures are generally quite difficult for historians to discuss as so much of what we do depends on written sources.