Online message taking precious time (5)

I believe the answer is:

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'online message' is the definition.
'tweet' can be an answer for 'message' (type of online message). I'm not certain of the 'online' bit.

'precious time' is the wordplay.
'precious' becomes 'twee' (I've seen this before).
'time' becomes 't' (abbreviation).
'twee'+'t'='TWEET'

'taking' acts as a link.

Can you help me to learn more?

(Other definitions for tweet that I've seen before include "online comment" , "delivered by a chirpy type?" , "Note from flier" , "Short message on a social medium" , "Birdsong" .)

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