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

I believe the answer is:

good omen

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

'a propitious sign' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'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.

Can you help me to learn more?

Want a hint initially instead of a full solution? Install my app