We were discussing German navy in South America not too long ago. I wonder if this involves the same actors?
The article above is pretty long, which is why I do not think I came close to quoting 1/3 of it. Anyway, it and the corresponding article on the Battle of Coronel go into considerable detail about what Von Spee was doing in his cruise from Tsing Tao (modern Qingdao), across the Pacific, and into the Atlantic. While he dispatched light cruiser Emden toward the Indian Ocean, he basically collected a couple of other light cruisers on his way to the Falklands, one of which I think had been operating independently off the east coast of South America, and possibly another that had been operating off the west coast.
I'm not sure whether Spee thought to reach Germany or whether he wanted to wreak as much havoc as he could for as long as he could until finally being sunk.
BTW, the Battle of Coronel, which was off Chile, was almost mirror image, technologically, from the Battle of the Falklands. The British force at Coronel was centered on a couple of obsolete armored that had been brought out of reserve and manned by incompletely trained reservists. Spee's armored cruiser, while an obsolescent type, were much newer, had been in active service, were much more heavily armed, and were some of the best in the German fleet when it came to gunnery. Until finally dispatching to deal with Spee, the RN had not sent anything like their best ships to the waters off Chile and Argentina.