The 'dungeon' entries for the books are actually just monster kills - you get credit when you kill the boss of the dungeon with the relic equipped, and they'll even have the book target icon over their healthbar like the other enemies for books. You can do them undersized, as well.

Light farming definitely doesn't work with undersized, although they did double the rate of light gain (again) with 3.0.

Someone else will have to clarify if the Zodiac dungeon drops can be acquired with undersized - I'm not bothering with that until I have a -lot- more gil, and the only drop I did get so far was in HM roulette.