I have two appleid’s both with 2FA. Primary (iCloud) for email, contacts, etc and a second one only for iTunes store (have had both for many years). I have reset the Apple tv and entered the primary appleid and verification worked ok (3rd gen now comes up with a verification window which is helpful).
However when I go to enter the iTunes store apple id (on the apple tv) I get through to the code verification entry dialog but don’t receive a code anywhere to enter and can’t find any method of generating one. All the instructions on the web, apple support documents and Glen Fleishman’s excellent book “Your Appleid” appear to only work with with generating a code for my primary apple id. (I can log in to my iTunes store from iTunes and web login (with verification code sent to my phone)).
Any Ideas?
Just a little curious as to why you used the iCloud apple ID initially, and not the iTunes apple ID? All of your purchases and payments would go through the second one, I’d have started with that one. Tempted to advise you to reset back to factory settings and to log in with your iTunes one. I think what you’re currently doing might be possible within an iCloud Family plan, logging in under your iCloud ID with your iTunes ID being designated as a family member.
Try generating a code on your phone manually (even though it may seem it should be for the other Apple ID).
Just a little curious as to why you used the iCloud apple ID initially, and not the iTunes apple ID?
I didn’t think of that - will try next opportunity.
I tried that and it didn’t work.