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 don't know anything about this answer so I can't tell whether this works.

'go on about the dome' is the wordplay.
'about' means one lot of letters goes inside another.
'on' placed around 'dome' is 'odomen'.
'go'+'odomen'='GOOD OMEN'

'being' is the link.

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