Well, I kind of found an answer to my own question. A paper by Dwyer, Farroukh and Khorsani suggests one of two things. Either,

A.) Scythian contact brought chainmail into the Parthian Empire. Celtic contacts with the Scythians meant a trade in armor, and some early archaeological digs in Eastern Europe suggest that chainmail was employed by Scythian groups as the 5th century BCE, though I'm not sure there was extensive (or any) native manufacturing in the period. But essentially, that war, trade, migration, etc., then brought this style of armor to the Iranian plateau where it was adopted by a large & sophisicate metalworking culture under Parthian rule.

or

B.) That Celts (Galatians and others) in contact with the Hellenic kings introduced it into Iran through their wars and other contact with the Seleucid Empire, and because it saw use in the Seleucid armies, it became part of the material culture of Iran, Central Asia, and parts of the Near East as well. By the Sassanian period, where contact with the mail-wearing Romans was also commonplace, it had become fairly common.

Kind of an incomplete answer, but it's at least a start. It's interesting to me what these kinds of items tell us about the movement of material goods and culture, and how mail armor may have traveled the path of the later Spangenhelm, adopted by the Germanic peoples from Hunnic, Scythian and therefore (indirectly) Persian sources, in reverse.

Here is a link to that article: https://journals.ekb.eg/article_137688.html