Question: Is there any verse in the Bible that says anything about the split between conscious and unconscious mind?
The Bible is filled with distinctions between conscious and subconscious. However a clear demarcation in the original languages is not always clear as the those precise terms were not used. In English we often refer to our subconscious with other words and it is the same way in Biblical Hebrew and Greek
For example εβουλομην often means 'consciously purposed' as here:
On the converse θελω often means 'subconscious desires' as in this verse:
According to the TDNT by Gerhard Kittel:
However just as in English these words tend to overlap and can be substitutes for each other. Phrases like 'having a desire', 'seeking', 'wanting' or 'purposing' or 'being ready or inclined' may have to be assigned to the conscious, subconscious, both, or neither, depending on the context.
2 Peter 2:12 talks about unrighteous men who indulge the flesh. The verse describes them as "creatures of instinct" and "unreasoning animals".
It seems significant that they are described as being moved by "instinct" rather than "reason".
This seems to indicate that it is error to be led by the "unconscious mind" at the expense of the "conscious mind".
I'm not sure "walking" should be classified as "unconscious", though; indeed, if it were, you may walk into traffic without thinking, as a sleep-walker might. ;p
The verse that stands out for me here is Psalm 32:9:
I read it as: "don't just go on autopilot or on habit, following the crowd. God gave you a brain, use it!"