Going over border, bad time to make journey (10)

I believe the answer is:

pilgrimage

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'journey' is the definition.
(I know that pilgrimage is a type of journey)

'going over border bad time' is the wordplay.
'going over' is a reversal indicator.
'border' becomes 'lip' (I've seen this in another clue).
'bad time' becomes 'grimage' (I can't explain this - if you can you should give a lot more credence to this answer).
'lip' in reverse letter order is 'pil'.
'pil'+'grimage'='PILGRIMAGE'

'to make' is the link.

Can you help me to learn more?

(Other definitions for pilgrimage that I've seen before include "Religious traveller's journey" , "special journey?" , "What Chaucer,s travellers were engaged upon" , "Holy journey" , "Religiously-inspired journey" .)

I've seen this clue in The Telegraph.

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