The most common and most likely answer to this crossword clue is the 6 letter word QUIRKS
I've seen this crossword clue in The Times
Q
U
I
R
K
S
Buddy explains!

The straight part
We know that "Eccentricities" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eccentricities = quirks.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 QUIRKS mean?
QUIRKS noun- An idiosyncrasy; a slight glitch, mannerism; something unusual about the manner or style of something or someone
- An acute angle dividing a molding; a groove that runs lengthwise between the upper part of a moulding and a soffit
- A quibble, evasion, or subterfuge.