I think there are something hidden in the tyger tyger poem if you compare together with the lamb poem:

"The Tyger" is the sister poem to "The Lamb" (from "Songs of Innocence"),
a reflection of similar ideas from a different perspective (Blake's
concept of "contraries"), with "The Lamb" focusing more goodness. "The
Tyger" presents a duality between aesthetic beauty and primal ferocity.
The speaker wonders whether the hand that created "The Lamb" also
created "The Tyger”

Seems that patrick jane is the lamb and red john is the tiger. So, we can relate red john with "primal ferocity", but with "aesthetic beauty"?