Ketchup is tomato-based so slightly acidic (as is human skin and hair), and also red is the complement of green, so should cancel it out somewhat.

Every hair dye box I've ever seen (yes, I read strange things when killing time in the supermarket) says to "test a piece" first, as everyone's body chemisty is different, and it's better to find out on a small piece of hair that your whole head what the dye will do to your particular hair!

Be careful, too, as dyeing hair too often can damage it, make it brittle and dry. I learned that at my very first job - worked at a wig shop, and that was a common reason for healthy women to look at wigs - over-coloring, or coloring then perming then coloring ... left their hair damanged and easier to cover completely than fix!