Here's a breakdown:
* As a general term: "Ancient American Indian villages" would not be capitalized. This is because it's referring to a broad category of villages, not a specific name.
* As a specific place: If you are referring to a specific village with a known name, such as "Mesa Verde" or "Cahokia," then you would capitalize the name. This is because you are referring to a proper noun.
* As part of a historical period: If you are referring to a specific time period, such as "the Ancient American Indian era," you may capitalize the term "Ancient American Indian" to make it clear that you are referring to a specific historical period.
Ultimately, the best way to determine if you should capitalize is to consider the context and whether you are referring to a specific place, name, or time period.