The eyebrow test is bogus. Many women routinely use eyebrow pencils, especially if their brows are too light to see. I’m a ginger, and I do the same, but use more of a natural “ginger hue.”
Having said that, it does look like a fake color. Most natural hair has a combination of several different hues and highlights. Gingers’ hair also tend to lighten with the sun, so in the summer the top layers are a bit lighter than the under layers. I call that fake simply because it’s so monochrome.
Our youngest is a bright red/orange ginger. Eyebrows & lashes are invisible without enhancements. I’m guessing you know when you are down to your last gallon of sunscreen - she’s the first to let us know.
Long sleeves in summer & big floppy hats, too (along with that gorgeous hair comes the very fair skin & freckling)