Private dance recalled by one on vacation (2,3)

'private' is the definition.
Both the definition and answer are singular nouns.
Maybe there's an association between them I don't understand?

'dance recalled by one on vacation' is the wordplay.
'dance' becomes 'jig' (jigging is a kind of dancing).
'recalled' says the letters should be written backwards (to recall can mean to bring something back).
'by' means one lot of letters go next to another.
'on vacation' says to hollow out the word (remove centre letters) (after the inside letters have vacated the word).
'one' with its middle taken out is 'oe'.
'jig' in reverse letter order is 'gij'.
'gij'+'oe'='GI JOE'

Can you help me to learn more?