Time on duty sees pet timer (3-5)

I believe the answer is:

dog-watch

I'm a little stuck... Click here to teach me more about this clue!

'time on duty' is the definition.
I don't know anything about this answer so I can't judge whether it can be defined by this definition.

'pet timer' is the wordplay.
'pet' becomes 'dog'.
'timer' becomes 'watch' (I can't justify this - if you can you should give a lot more credence to this answer).
'dog'+'watch'='DOG-WATCH'

'sees' acts as a link.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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