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Since your repair would be to the area of the apron, you could get a good match for coloring. What you likely did was abrade the area too smoothly, which would make stain penetration difficult. You might try sanding with 180x-220x, and fade out the edges of the sanding area so you don't have a sharp sanded line next to a colored area. Sand only with the grain.
If you have a very soft paint brush, maybe only 1" wide with long hair bristles, there is a technique you could try. If you don't have a good brush, pick up a woman's make-up brush. The one she dabs in the colored face war paint (maybe called blush) and whisks it over the skin. It might look like a shaving brush. Very soft bristles. You can snip off the outside rows of bristles until you have a nicely shaped straight brush.
If you have already tried a stain (the one that didn't take), and it's an oil base stain, take the can and stir it well. Have a clean cloth ready, and get some stain on the brush and let it flash dry off for a few minutes. Then lightly whisk over the bare area with the grain. You might try this on a sample first, but if you can get the hang of this, it's really pretty easy.
If you want to try a gel stain, and you have the right color, read the directions, as each brand may differ. But, basically, the way it works is you brush it on (some may have a flash time of a few minutes), and then wipe/brush it off to the intensity to match. The more it's drawn off, the lighter it will get. It would be to your benefit to also try this on a sample. If you have no wood scraps, use cardboard.
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