This is someone who influences or controls a public figure behind-the-scenes.
In 17th century France, Cardinal Richelieu was known as “The Red Eminence,” because of his position in the church and his red robes. However, many thought he was heavily influenced by an assistant who who different colored robes. That person was referred to as “The Gray Eminence.”
“Éminence Grise” is a direct French translation of “gray eminence.”
I feel like the “gray” adjective also describes someone operating “from the shadows,” but perhaps that’s just my personal perspective.
Sometimes also called “the power behind the throne.”