John, I think that the general idea that the 7.9x57 S cartridge was not used in South America originates from several of the most well known books dealing with Mauser rifles used around the world. For example, almost without exception, you will read that Ecuador used vz. 24 rifles chambered for the 7.65x54 Mauser; however, this is a mistake as the 1936 contract specified that all 30,000 rifles were of “7.92” caliber. The same mistake occurs with the ZB 30 machine gun, as all 750 units purchased that same year from Brno were also specified as “7.92” caliber.
Regarding the ammunition for these arms, it was also bought from Brno and is packed in 15 round boxes with an orange label that reads: “Z BRNO 15 Cartuchos Mauser 7.92”. Typical headstamp is 19 / Z / 36 / III / and maybe also 19 / Z / 37 / IV /.
Also, is worth mentioning that the Argentine cartridges were packed in two different ways: in clips for rifles in crates marked “7.92-F.” (F. = Fusil) and without clips for machine guns in crates marked “7.92-F.A.” (F.A. = Fusil Ametrallador or maybe Fusil y Ametralladora). Because of the lack of clips, the crates also have a difference in weight of 1.5 kg (34 vs. 35.5 Kg).
There are at least two other countries that in 1937 purchased small quantities of Czechoslovakian vz. 24 in 7.9x57 S, these being El Salvador and Nicaragua. Also, Venezuela purchased ammunition from Kynoch before and after WWII.
For the moment, I don’t know of any other that used the “S” round, although many South American countries seems to have had at one time or another rifles chambered for the M88 cartridge.