The most common and most likely answer to this crossword clue is the 8 letter word DARKENED
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "became dim" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case became dim = darkened.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 DARKENED mean?
DARKENED verb- To make dark or darker by reducing light.
- To become dark or darker (having less light).
- To get dark (referring to the sky, either in the evening or as a result of cloud).
- To make dark or darker in colour.
- To become dark or darker in colour.
- To render gloomy, darker in mood.
- To become gloomy, darker in mood.
- To blind, impair the eyesight.
- To be blinded, lose one’s eyesight.
- To cloud, obscure, or perplex; to render less clear or intelligible.
- To make foul; to sully; to tarnish.
- Made dark or lightproof by the exclusion of light