There are standards relating to pens and ink. ISO 12757 (which as I understand it has replaced DIN 16554) and 14145.
12757 is about the properties of ballpoint pens and refills and how to test them. 12757-1 is about the dimensions of refills (for example a G2 is a "Parker style" refill) and quality for general use. Part 2 is about the requirements (light fastness, water resistance and shelf life) for documentery (DOC) use. If you're looking for archival ballpoint ink, then it's ISO 12757-2 you want.
ISO 14145, part 1 and 2, are about the corresponding hings for rollerballs.
Doesn't seem to be one for fountain pens, which makes me suspect they aren't really approved for documentary use, although there likely are inks which could be if their makers insisted on it and ISO had a category for it.