The most common and most likely answer to this crossword clue is the 6 letter word TAPERS
I've seen this crossword clue in The Times
T
A
P
E
R
S
Buddy explains!

The straight part
We know that "Gradually reduces/feeble lights" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gradually reduces/feeble lights = tapers.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 TAPERS mean?
TAPERS noun- A slender wax candle; a small lighted wax candle
- (by extension) a small light.
- A tapering form; gradual diminution of thickness and/or cross section in an elongated object
- A thin stick used for lighting candles, either a wax-coated wick or a slow-burning wooden rod.
- One who operates a tape machine.
- Someone who works with tape or tapes.