Chris Spencer’s Who’s Who of Aussie Rock (5th ed 2002, p 46) only has two “Book of” band entries.
The first is BOOK OF FUNK (1990-93), and he says they began in Perth before moving to Sydney.
The second he has is BOOK OF LOVE, and the only info he has for them is a vinyl single “Lullaby” (Sept 1988)
Discogs gives 10 results for bands beginning with “Book of” but NONE are Australian
RYM gives a few more, and again, NONE are Australian.
Both sites DO have Book of Love, but as an AMERICAN band and they did put out a single Lullaby!
https://rateyourmusic.com/artist/book_of_lovehttps://www.discogs.com/artist/50714-Book-Of-LoveI think this may be the band he is chasing.
It seems they
may have featured on the Beverly Hills Cop soundtrack, because Discogs has an Italian promo 12 inch: The Heat is On (Glenn Frey) / Boy (Book of Love)
https://www.discogs.com/Glenn-Frey-Book-Of-Love-The-Heat-Is-On-Boy/release/2390163Cheers,
Oz