Fishermanbt, what you've done for prepping the tails is fine, What toadfrog said about getting dyes & dyeing is spot on too. Rit Dyes can work, but they're not specifically formulated for protein based materials. Dharma Trading sells acid dyes, both their own brand, and Jacquard brand. It may depend on the exact colors you want which is a good choice, but last I bought dyes, there was not a lot of overlap in colors.
I've had the most success with dye bath temps in the 165 to 185 degree temp range and I've dyed many types of hair/fur and feathers.
The only thing I don't necessarily agree with is long soaks in a dye bath or to clean, as that can cause the hair to slip. However, spending time cleaning what you're dyeing will provide the best results as clean material will absorb dyes better than dirty, oily or greasy.
The last materials I dyed was some Fox & Coyote tails, which are a bit trickier than deer tails since the hides are much thinner. That's when you really have to pay attention to dye bath times. I've had the hide literally dissolve.
This was one of the tails I dyed, looking to get a "greenpumpkin" color for tying fly patterns and hair jigs. I mixed Dharma avocado with a Jacquard brown. As you can see, it's not all one color, and different shades because the base color was not all the same. White is a bit easier to dye over. I was however, happy with the result as I dyed several tails and got what I needed plus some other useful dyed olive green shades of hair.