What I do is when the stock surface is ready, slop the stain on heavily. Get it wet, and keep it wet for a while to let it all soak in. Then set the stock aside to dry for at least an hour. You should be able to see the color change. Sugar maple will tend to turn gray. Red maple may tend to turn more greenish. (If you're using something like the Wahkon Bay stain, it has HCl in it, unfortunately, which is not needed, and tends to make a green color that does not like to go away. I would not use it, myself.)
When the stock is dry, heat it carefully with a heat gun. A radiant heat is better, but it can be hard to hold the stock and move it around over a stove burner plate! You can watch the stock turn color as you move the heat over it.
Now, I have a hard time seeing imperfections in the surface when the wood is still white, so I will often see little places that need to be fixed after stain is applied, so I will fix them and then stain again (it needs more than one application anyway). You can also "whisker" the stock here, as necessary. The stain does not continue to get darker with each application, but it may require several applications to get even coverage, especially if you've been having to fix places on the stock like I do. Actually, you can apply the stain so much, that the stock begins to be saturated, and you will have difficulty even getting it to soak into the wood at all.
When done, neutralize and then wash it all off. Let it sit for a good while to dry out and it's then ready for finish.
Aqua fortis will change the color of the wood more than just depositing a pigment in the grain. The wood remains clear and bright and natural looking, unlike with modern dyes and stains.