So you have a '99 or 2000 Tiger? Good bike. Much better than the original 855 carb'd Tiger. Your bike has a better head and valve gear. I put 35K miles on my '99 Tiger, no problems and it's still running far as I know. (sold it) Take care of it and it will be fine and should make a 20,000 mile S. America trip.
Keep the valves adjusted, change the oil every 3 or 4000 miles. Do a really good service on the bike, new Iridium plugs, have Triumph load a nice fuel efficient Tune into the bike, make sure wheel bearings are OK. Start with new chain and sprockets, new tires/tubes, double check nuts and bolts. You're good to go.
The Tiger is a bit tough to handle off road but no worse than any BMW twin. Go with TKC 80 Conti tires and go. Don't over load the bike. The suspension is great on the rough S. American roads and non roads. My Tiger got decent economy, could go about 180 to 200 miles on a tank.
Learn as much as you can about the bike before you go. Put together a really good tool kit, including tire changing stuff.
Don't sell it! If it's in good condition, take it. But know that after S. America it will be well used!