In case you fly and are back within the time of your TIP and assuming that you have enough time to exit from Peru to Bolivia or Chile or Ecuador, then you dont need to suspend the TIP.
For long term storage it makes sense, but for a 2 week trip back home, you dont need to deal with so much bureaucracy.
Your vehicle is not linked with your passport, so the local authorities have no clue if you flew out for a couple of weeks and returned. Same goes for Colombia.
Its a common practice for lots of travellers.
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