Sounds like you need narrower tape - 1/4" or 1/8". Tamiya masking tape is excellent; I don't remember what the thinnest width is, but it's somewhere in that neighborhood - and quite flexible. Or you can lay the stuff you have down on a piece of glass and slit it.
The real narrow pieces, of course only need to go right next to the line. You can lay full-width strips of 1/2" (or wider) tape alongside it to cover the rest of the necessary area.
Hope that helps. Good luck.