There is no bracket. The trunk lock cylinder goes into a chrome housing which is retained by 3 spacers and nuts on the studs attached to the chrome housing.
If that's not what you're talking about, maybe you could be more precise in your description. The only other thing I can think of that you might be referring to is the square tube that is attached to the tail panel bracing that the trunck latch hooks on to in order to keep it closed.
Still not following you. Are you talking about the chrome piece with cougar spelled out on it that flips up to insert the key into the lock. If that's the piece that wont stay attached, there is a small spring that goes on the post attached to the flip up part that holds it to the chrome base. If that's not what you're trying to describe then you're going to have to post a picture.