There is a lot of poor information surrounding this process. What you are doing is making a salt of iron or iron acetate by mixing the steel wool and vinegar. You do not need to let the steel rust first, in fact it will give you poorer results as the rust has changed it's state. Vinegar plus Iron (Fe) makes a Ferrous acetate, Vinegar plus Rust creates a Ferric acetate. The main difference for our purposes is that Ferric Iron Acetate is NOT water soluble; Whereas Ferrous Iron Acetate is. Vinegar is a solution in water so obviously we want the water soluble version. If your solution is very reddish brown that's a big indicator that you have far more of the non-soluble solution.
So this means that you need to use clean, non-rusted steel wool or other high iron content metal, and clean vinegar. It also means that once your solution has properly "cooked" you can filter it and store that solution for quite a long time before using it.
The Iron Acetate reacts with tannin as we know to create a dark black color. But the tannin it reacts with does not have to be naturally in the wood. You can take any wood, add tannin to it, and then ebonize it. I touched on how to do this above. The color of black that this produces is a more natural looking black than you get from any dye, pigment stain or other chemical process; it seems to be a more neutral black on the color spectrum while the other methods will often have a distinct sheen of a different color. With that said, sometimes ebonizing + a thinned dye will give you the particular black you are looking for. Another option is to simply repeat the process a second time. If you ebonize and it's not black enough, wash the surface with a tannin heavy solution, wait and hour, and ebonize again. This will give you a deep BLACK on almost any wood.
When using standard white vinegar it's not necessary to neutralize the wood before finishing, but it won't hurt either. I know some use a highly watered down ammonia for this.