Honestly, with the wide variety of different colors or appearance of authentic, aged, military configuration Krag rifles and carbines, I don't think you need to reproduce the exact original stain used 120 years ago. I have a number of Krags, as do many others on this forum, and most of them, side by side, look different. I use staining to try to best match the specific firearm stock I am working on for consistency of the different parts. I hate seeing a Krag that has a dark stock and a light hand guard. I have actually passed up purchasing some nice Krags because they appeared to be mismatched in their stock parts. That's a dead give-a-way that it has been pieced together at some point.

So, you don't have to reproduce the original color of stain to be authentic or correct.

Others can chime in to help. I have not studied the original staining process as much as some other Krag-philes, so, your question may be answered better by someone else. I just wanted to add my 2c worth of experience!