The use of the term Drawing Down the Moon thus has no connection to the ancient practice, and is used in the Wiccan tradition as the poetic description of the process of invocation of the goddess into the High Priestess.
In recent decades the ceremony of Drawing Down the Moon to invoke the goddess has been supplemented by the ceremony of Drawing Down the Sun to invoke the god. So as a final observation on the ceremony of Drawing Down, we may note that this too is not a new idea or term, as the ancient Greek philosopher Plutarch wrote many centuries ago:
“What is this but, like the Thessalian women, to call down the Sun and Moon by enchantments from the skies”
 Morals, vol 3, Plutarch, circa 100 CE
Extract from: Wicca: Magical Beginnings written by d’Este & Rankine, 2008 (Avalonia.) PB / Kindle @ https://amzn.to/3Ay4HJr. Shared here with the intention to inspire and inform the now and future generations interested in Wicca and other Pagan traditions inspired by it.