I make a post every few months when I do this so just letting other Gringos know how it goes.
Firstly, CAREFUL IF YOU HAVE OVERSTAYED!
I got refused from all the buses crossing and the first few collectivos because I had overstayed (only by a week) because they didn't want me to delay the rest of the people, or slow down their money making, and some seemed to say there was nowhere to pay on the border. General misinformation. Even the police weren't sure. General confusion all round. Probably down to not many gringos crossing. I ended up going to immgration in Tacna to try and clear things up but got the usual "the person concerned will return from lunch in 3 hours".
After heading back to the international bus terminal luckily a really efficient collectivo driver said yes and really helped me out.
Turned out it was no effort at all, there's a Banco De La Nacion at the crossing right by where you get your passport stamped that only had one person in the queue.
So my route was: Lima - Cruz del Sur to Tacna > Tacna - Arica collectivo
Would have been a breeze if not for my overstay.
CONTROVERSIAL OPINON ALERT: THE ECUADOR-PERU BORDER IS SAFER AND EASIER
Now that they've built a proper crossing point.
1. It's full full full of gringos. The Tacna-Arica I saw no other gringo . Peru-Ecuador the bus is sometimes half gringos
2. It's easier because of CIFA. CIFA are used to Gringos and don't bat an eyelid. Tacna-Arica no one not even the police know if you can pay at the border.
3. Payment for overstaying is easy. You just pay to the official and pay whatever the amount while getting your passport stamped. In Tacna-Arica you have to go to the Banco de la Nacion and it takes longer and they give you an official overstay stamp and use IN TOTAL ONE PAGE OF YOUR PASSPORT (fine as mine is expiring but wow i'd be angry if it was new)
Just to note: i haven't really border hopped as I'm still in Chile but I'll be returning to Peru once my Visa is up