So, Borges and the mirror animals...
I've gone through thirteen of the twenty-three books written by Herbert Allen Giles. So far, no mention of animals in mirrors. The other ten don't look promising.
I've gone through one of the Fontecchio books, and nothing.
Andrew Hurley, who translated the edition of The Book of Imaginary Beings I've got, provides notes on the sources Borges (and co-author Margarita Guerrero) used for his creatures. Those notes conveniently skip the mirror beasts.
Sorry about the misleading title to the post. No clues yet.