Once upon a time I read in an old book on home economics that if you wind up the yarn before dyeing it into a ball, it will be painted over with a smooth transition from the natural color of the yarn to the natural color of the paint - more intense outside the ball, weaker inside the ball, that is, with a gradient ... It was recommended to wind the beginning of the ball more tightly, gradually reduce the density, and by the end of the ball, wind the yarn very freely.
I also use food dyes a lot too, like the ones for Easter eggs, or buy aniline dyes from Leonardno's store. To fix the paint, I take ordinary table vinegar.
To dye yarn with a gradient transition, I wind the yarn into a ball, immerse it in water so that the yarn gets wet, then wring it out and immerse it in the dye solution.
As you can see, the technology is quite simple, but there are some nuances. The color gradient is obtained due to the fact that the paint is perfectly absorbed by the upper layers of the ball and very poorly reaches its middle, i.e., the intensity of staining the ball greatly decreases towards its center, and if the ball is still tightly wound, then the ball from the inside may not stain at all. Therefore, lately I ignore all the recommendations for reeling a ball for coloring, replicated on the Internet, and prepare a rather loose ball (but by hand, not on a winder). The optimum weight of the ball for one-time dyeing is 75-100 g. With a large weight, do not dye the ball to its core.
Another nuance is that with such a size of the ball, we can never be sure whether we have enough intensively dyed yarn for the last rows (this is if we knit a shawl from top to bottom and start from the light section of the yarn). As a rule, I miss quite a bit - 35-50 meters. Therefore, when dyeing the ball, I put a small skein in the same vessel with dye, and it certainly gets dyed 100%. To create some "unpainted" in this small skeleton, you just need to tie it with threads in several places, and not even tight