historically "wired into [the brain]" as a synonym for "connected to" is rare, with the only references seeming to be electrification/telegraph connection [1913 newspaper, "Wired Into Nature", a book about frontier telegraphy in the US]
"hard-wired [in the brain]" arise after the computing use of "hardware" in the 60s, and seems from the beginning to be used as a psychological metaphor. (except for those links above, all references are from the OED)
"hardware" and "software" themselves date to at least the 15th century, being used to describe consumer products (utensils/tools vs woolens/linens/food). and the people who made them ("hard-ware Mechanicks"). "hardware" had some connotations of gender: the "hardware lads" of 1831. In the US "hardware" used to mean "hard liquor", and still did regionally up to 1967. Use of "hardware" to describe computer components first occurred in the seminal ENIAC paper, and predates the use of "software" (though by the late 50s "software" seems to have been the term that first came to writer's minds, with "hardware" used as contrast).
My guess is that "wired into", deriving from telegraphy/telephony metaphors, came from Pavlov (who used those to great effect), and only 50 years later encountered the term "hard-wired" coming from computing, whereafter the two were used together, and potentially interchangeably despite their different origins. Of course, they mean quite different things; "wired into" posits wires as mutable and an agent of change, while "hard-wired" uses them as something fixed and intrinsic.
I also wonder if "wired into" was ever used in the context of wire-wrap computing, where wires could have been meaningfully divided into "soft" vs "hard". Maybe the computer-brain metaphor we're always making is at its core still an archaic wire-wrapped Lisp machine?