Most builders who want a "string" line, glue on a super thin strip of contrasting wood. It's actually easier. Since you mention that you are going to stain, it adds a major problem. You can try masking and rub on stain with a Q-tip along the edge and then do the other side. Stain will not travel through the glue line.

BTW the video is exactly how a crack in a guitar top it fixed except they cut right through the wood and fashion a tapered matching piece that gets glued in. Notice they use holly in the video - it's the whitest of woods.