Step 9: Glue it!
Mix up a dab of epoxy. (Don't use super glue for this, it's too brittle and doesn't give you time to position the bracket.) You don't need massive globs of it. I mixed too much, and used the excess to "repair" a rock hole in a headlight.
Pull the assembly off of the antenna. Carefully, using a toothpick or a nail or something, dab a little epoxy onto the wire wherever it touches the antenna housing. Try to avoid getting it where it'll show.
Then set it back where it was, re-apply the duct tape, and leave it alone while it cures.