Hi Philip. I have used TB III to glue fretboard to necks as well as most of my cbg gluing requirements through 2 big bottles. I have not observed the black line you describe. My wood is mostly red oak (necks and fret boards), a little poplar, and scraps of other stuff laying around. Wonder if the wood you use might have a hand in your negative effect? Not shillin' for TB3, just wondering.
I don't have observed the black line you describe neither, my necks are beech tree and it's even hard to check where the joint is.
TB lll dries darker than Elmers and if the joint isn't tight you might see a line of the glue there making the line. When joints are tight it never shows. TB lll is all I have ever used and it works fine when I pay attention to quality in my work, if not then I get what's deserved.