The most common and most likely answer to this crossword clue is the 4 plus 11 letter word WORD ASSOCIATION
I've seen this crossword clue in Financial Times
W
O
R
D
A
S
S
O
C
I
A
T
I
O
N
Buddy explains!
The straight part
We know that "Unconscious insigh/ts/ gleaned from this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unconscious insigh/ts/ gleaned from this = word association.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.