I'm willing to give them a little more time to follow some proper procedure and to not have to invoke a CC chargeback, but they're making it difficult.
I just received an email followup:
"Dear <TA>,
Thank you for contacting TAP Air Portugal.
We apologize for the inconvenience experienced in trying to contact TAP Air Portugal.
Kindly help us with the following information so that we can process the refund:
Account Holder Name
Name of Bank
Bank Country
Routing Number
Account number
Address
City
Local Zip Code
State
We are looking forward to hearing from you.
Thank you for your loyalty to us. "
Are you kidding me. Asking me to send this over email. And I paid with a credit card.