The most common and most likely answer to this crossword clue is the 8 plus 5 letter word NONSENSE VERSE
I've seen this crossword clue in The Times
N
O
N
S
E
N
S
E
V
E
R
S
E
Buddy explains!
The straight part
We know that "There may be rhyme but no reason in it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case there may be rhyme but no reason in it = nonsense verse.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.