Openly enjoying a stay in the country? (7,3)

I believe the answer is:

camping out

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

'openly enjoying' is the definition.
I can't tell whether this defines the answer.

'a stay in the country?' is the wordplay.
I cannot quite understand how this works, but
'a' could be 'amp' (A is the symbol for the amp or ampere) and 'amp' is found within the answer.
'in' is within the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Globe and Mail and The Irish News.

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