As it happens, I am in Iquique, and the couple I am with tried to buy new tires here, for a BMW R80 GS and a Suzuki 650, and had no luck. They are now looking for a second day, but we're pretty sure they'll have to limp along to Antofagasta (450 km south), where the Chileans we've talked to said there probably will be some. They had particular difficulty with the rear tires - no 130/80s here at all and nothing in the size of the rear for the Suzuki (don't know the measurements but it is a 17 inch wheel.)
They said that there were some front tires, but they are total road tires.
Watching white moon face,
The stars never feel anger,
Blah blah blah the end.