Columbia, you’ll need both an overflight and landing permit. Now, if you're just touching down for less than 48 hours at the same airport, I think you can bypass the permit requirements.
CAA of Colombia at:
+571 296 2208
sobrevuelos@aerocivil.gov.co
The situation’s similar over in Ecuador, too. The DGAC Ecuador is your point of contact:
+593 2 2947 444
uio.sobrevuelos@gmail.com uio.sobrevuelos@aviacioncivil.gob.ec
Peru, give them a three day headsup. You’ll need to fill out specific forms depending on the nature of your flight. For overflights, it’s FORMULARIO DGAC 1, and for private landings, it’s FORMULARIO DGAC 2.
Direccion General de Aeronautica Civil at:
+511 315 7800 ext. 1192
+511 315 7881
dgac@mtc.gob.pe
A couple of words of caution, if you don’t mind me saying. Keep an eye on 121.5, as these areas can be a bit trigger-happy. You don’t want to be mistaken for a drug runner, even though an RV doesn’t exactly carry a hefty load for that sort of thing.
Also, you’ll find the radio repeaters are on in many of these places, which means you’ll hear the controller’s voice with some serious reverb. Be sure you’ve got a good EFB app that shows you the correct frequency, in case the controller or yourself miss a frequency hand-off.
I'd recommend keeping a close eye on all fueling and handling. As you know, it's better safe than sorry.
Now, file a flight plan always.
you can’t always file electronically like we do back home. But most apps will generate a PDF of the ICAO flight plan, which you can send over to the FBO and have them pass it along to the tower.
Lastly, it wouldn’t hurt to carry some basic tools, spare tubes for a flat, a PLB beacon, and some essential survival gear. A translating app that can handle both text and images will be mighty useful if you don't speak the local language.