In some cases, the false teaching that the Biblical author is responding to is in the text itself. For example, there are a few instances in Romans where some conclude that Paul is using a rhetorical device to talk as if he's one of the false teachers, which he then responds to in order to correct that view:
- Romans 1:18-32 e.g. "and the men likewise gave up natural relations with women and were consumed with passion for one another"
- Romans 7 e.g. "For I do not do what I want, but I do the very thing I hate."
- Romans 3 e.g. as dialogue "Then what advantage has the Jew? Or what is the value of circumcision? Much in every way."
It is beyond the scope of this post to determine whether that is actually the case or not, but if it is the case in each of the above instances, I would consider them to be "embedded mirrors". In other words, Paul is stating the false teachings that he then responds to.
There may also be a similar device in Ecclesiastes. The "Teacher" may be giving the false teaching, who is then briefly corrected by the narrator at the end of the book. I don't think this is the case however, as I explain in my mirror-reading of Ecclesiastes here.
An example in narrative form is the Book of Job. Job, Elihu, Job's three friends and God deliver to the reader dialogues between the false teachings and the true teachings.