Does a database or dataset exist that lists all exact Degrees, Minutes, and Seconds (rounded to nearest decimal) for the continent of South America? What I am seeking is a list of DMS's that covers that entire geography; not just a few specific coordinates, but all of them. Given that each DMS represents ~60 nautical miles apart, the data shouldn't be overly complicated to form. The trouble is, I can't locate the consolidated data anywhere on the web!
Get boundary data for all countries in the region (can be downloaded from gadm.org)
Loop over all D/M/S on the earth, doing point-in-polygon tests over the boundary data from step 1 - this can be done using Python, R, Java or C or lots of other programming languages.
Keep those D/M/S values that are inside the boundaries.
How many points would you expect? The whole earth is 360 degrees round and 180 degrees north-south, so thats 360*60*60 * 180*60*60 = 8.4 x 10^11 points. South America is maybe 1/10 of the planet, so that's about 10^10 points - a few billion.
You'll end up with a table of a few billion points. I'm not sure how that would be useful, but that's how you'd do it.