The most common and most likely answer to this crossword clue is the 6 letter word CRANKY
I've seen this crossword clue in The Guardian
C
R
A
N
K
Y
More clues leading to the result CRANKY
Buddy explains!

The straight part
We know that "Eccentric" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eccentric = cranky.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.
What does CRANKY mean?
CRANKY adjective- Weak, unwell.
- (of a machine, etc.) Not in good working condition.
- Grouchy, grumpy, irritable; easily upset.
- Not in perfect mental working order; eccentric, peculiar.
- Full of spirit; spirited.