There are a few questions here aiming at improving the visibility and use of the tag wiki. Some of the suggested answers have been taken up, such as auto-completion when adding tags to a question.
I've not seen anyone suggest popping a tag wiki section into the FAQ. Currently there is one vague reference to "tag wiki" there and it's unlikely to pique the interest of new users since it refers to a privilege requiring 5k rep.
I've come to see the tag wiki as a kind of topic-specific extension of the FAQ. If this is a good way of looking at it, maybe the main FAQ should do more than just barely acknowledge its existence.
Among other things it is worth explaining to new users that they ought to read the full wiki text of any tags they propose to add as it may help improve the quality of their question and subsequent answers. I would also make it clear that the tag wiki is maintained by the community and make a note of any privileges related to that.