I am not a specialist, that said, I think walnut husk dye (I think it is known as Van Dyke crystals in English) could be a good option, perhaps it is what was originally used, it has been used for centuries (probably millenia) as a wood stain, ink, etc. It is lightfast. I use it very often.

You can make a mix from very light to very dark, and you can build up layers until you get the depth you want. It is water based, which is nice and easy, but also raises the grain a little. I don’t find that much of a problem, though. You can then flatten the grain back a bit rubbing with a bunch of straw.

You just mix the crystals, which are quite inexpensive (I find them in bulk at the local drugstore), with lukewarm water, until they are dissolved, and apply with a brush or a rag. Careful to work fast, in the direction of the grain, and not overlap partially-dried strokes, then you may get darker marks. It is a bit tricky to apply, it behaves a lot like watercolour.

Oh, I also use distilled water because the water in my area has a lot of solid impurities, but this is probably overkill.

I attach an example, I dyed these oak floorboards with one layer of rather concentrated stain. In this case I used a very wide brush in nearly one stroke.