Cute siren went off for a long time (9)

I believe the answer is:

centuries

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'for a long time' is the definition.
I can't judge whether this definition defines the answer.

'cute siren went' is the wordplay.
'went' is an anagram indicator ('go' can mean move).
'cute'+'siren'='cutesiren'
'cutesiren' is an anagram of 'CENTURIES'.

'off' acts as a link.

Can you help me to learn more?

(Other definitions for centuries that I've seen before include "Censure it for hundreds of years" , "Periods of 100 years" .)

I've seen this clue in The Mirror.

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