Papers knocked back article - press regularly vacillates (7)

'vacillates' is the definition.
Although both the answer and definition are verbs in their -s form, I cannot see how they can define each other.

'papers knocked back article press regularly' is the wordplay.
'papers' becomes 'ID' (identifying documents are one's 'papers').
'knocked back' says the letters should be written backwards.
'article' becomes 'the' (the definite article).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternate letters of 'press' are 'rs'.
'id' in reverse letter order is 'di'.
'di'+'the'+'rs'='DITHERS'

Can you help me to learn more?