TLDR - Eva Air can suspend your online account without notice; to speak to someone, call 1-800-695-1188 until it goes through; send verification documents to [email protected]
Hopefully this saves someone from pulling out their hair during the process!

Here goes...
I searched for this particular situation, but couldn't find anything relevant, so I'm posting this here for others who might run into the situation in the future.

So, me and my partner both registered for Eva Air Infinity MileageLands accounts recently with the intention of transferring miles from our respective Citi Thank You points accounts for a pair of Eva Air business class tickets (North America to Asia). My partner was going to be flying on United in a few days, so we figured that he could credit the miles to Eva and we could potentially transfer fewer points over. About 2 days after the United flights, I logged onto his account and noticed that the first segment had credited into Eva Air successfully, which meant that the second segment should be appearing soon. At this point, I initiated the transfers over from our Thank You points accounts. I knew that this is not an immediate process (I tested a transfer to my account a few days earlier, it took 36 hours; CapOne points was actually instant) so I was prepared to be patient. However, to my horror, the next morning I wake up to check, and a message appears on his account saying that the account online functions were suspended and to call customer service. It was nearly impossible to reach someone, the Taiwan Infinity office was closed, the US customer service line kept on telling me to call this other number for mileage plan issues, and that number would automatically disconnect after telling me they were all busy. After a few hours of trying every way to find someone to talk to, I was finally able to get through the US number (1-800-695-1188) by repeated dialing in. Apparently, something triggered a fraud or verification flag, and I would need to send in both his passport and his most recent United itinerary to [email protected] and that it may take maybe 3 business days to resolve. In the end, I think the account became useable within less than a day after I sent in the information. Phew! Fortunately our points transfers also came through around the same time, and I was able to successfully book the tickets. But, what an anxiety-inducing day!