After some further testing, I can't seem to figure it out; the knight's shield doesn't pass its affect to the duct tape, nor does amethyst and I don't think the cleaning rag works on it either...
The duck tape passes any effect that is placed on it on the first tiles above, below, to the left, and to the right, but not crosswise. Example 1: If an emerald were to effect the duck tape, if a weapon was beside the duck tape, even if not above or below the emerald, it would be effected by the emerald. Example 2: If an arrow were to be pointing at the duck tape, empty spaces that would not count toward the arrow's damage, would effect it if it were adjacent. Hope this helps.