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Well, for Pikachu/Eeeve you need to go to the Wild Area Station, not the Wild Area itself, so you probably get them there (inside) from some PC or NPC...
Since they're special, I'd say it works like Mew from LGPE, you get it one time with random nature and you're done, no way to farm or anything like that
Specially now that you can (presumably) change nature in the Pokemon Center