Encyclopedia.com has an article about dyeing hair in Ancient Rome that brings some references to the table.

I don't know if linking to pages with references is allowed in the subreddit, but I'll post the link here because OP may find them helpful: https://www.encyclopedia.com/sports-and-everyday-life/fashion-and-clothing/clothing-jewelry-and-personal-adornment/hair-coloring

I apologise if this response is not in compliance to the rules.