Go on about the Dome being a propitious sign (4,4)

I believe the answer is:

good omen

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'a propitious sign' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'go on about the dome' is the wordplay.
'about' is an insertion indicator.
'on' going around 'dome' is 'odomen'.
'go'+'odomen'='GOOD OMEN'

'being' acts as a link.

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