It may be worth you telling us why you want to ebonize it. The reason I say this is that years ago people tried to do this with all sorts of wood that they were trying to make look like ebony or rosewood, when the top quality stuff got in short supply for guitar fingerboards. (You can always tell, instantly).
Oak galls etc all work, but frankly I would probably use powdered food safe vegetable dye (cheap as chips and you need tiny quantities - often sold for staining ponds black) and make my own colourant. Various recipes available.
(spell check here, which enforces site choices, 2 clicks to get out of, drives me crackers)
You can get it on Amazon for wine making. They add it to get the oaked barrel taste I think. If there are any make your own type wine stores in you country they will have it too. Cost something like 5 or 10 pounds or so for a pound of the powder. Dissolve it in water and wet the wood good and let it dry. A few coats and then do the same with your vinegar and steel wool solution and it should blacken the way you want. If you were using oak you wouldn't need the tannic acid unless there was sapwood. Play with scraps to get the process down before putting it on the furniture.
I've used iron staining on a few different timbers, both timbers rich in tannin like Oak, and timbers that are low in tannin. The bottom line is that tannins evaporate quite quickly from the sawn surface, so even on Oak, unless it's a virgin surface fresh from the tool, you'll need to prime the surface with tannin in order to prevent a patchy finish.
You'll get a perfectly good result from making a brew of strong tea, or boiling up fresh Oak shavings, but if you want the absolute deepest black then hunt out Oak Galls to crush up. Where I live in the New Forest it's easy enough to collect pocketfuls of them. I believe in medieval times Oak Galls were used to make ink.
Couple of other tips.
-Add a single drop of washing up liquid into both your tannin and your vinegar/steel wool solutions, you need this to break surface tension and get the solution deep into the pores of the timber, especially important on a very open grained timber like Ash.
-Decent quality, un-oiled, steel wool seems to be thin on the ground these days, so you might be better using a handful of rusty old nails in your white vinegar solution.
-Personally I apply a couple of coats of both solutions, it doesn't seem to matter in what order.
-If there's an interim reaction and it goes a sort of dark burgundy don't worry. As soon as the final oil or wax or varnish coat goes on it'll go jet black, indeed a good burnishing with a hard bristle brush (which you should do before the final finish coat) is often enough to take it black.
Here's a desk that I made, Bubinga slab top with scorched and iron stained legs, it really was as black as pitch,