Cannot login to iTunes on a Second Generation AppleTV with Two Factor Authentication enabled for your AppleID

If you have two factor authentication (2FA) enabled for your AppleID, you will be unable to sign into iTunes on your second generation AppleTV without first performing some extra steps.

This is due to the two-factor code's thirty second time out; by the time you are notified on your trusted device that another device has attempted to sign in and are given an authentication code, the login on the AppleTV will often time out if you have to enter passwords via your AppleTV remote.

The solution is to obtain a 2FA Verification Code manually using a trusted device after you've typed in your password on the AppleTV, but before you click "Enter," then add the six digit code to the end of the password.

Follow the instructions here to get an authentication code on demand from a trusted device:

Get a verification code and sign in with two-factor authentication - Apple Support

Then::

1) Enter your AppleID password on the AppleTV iTunes login screen, but do not yet click "Enter"

2) Perform the steps above to obtain a six digit Verification Code

3) Append the received Verification Code to your entered password, then click "Enter."

For example, if your AppleID password is "My2019AppleID," you would enter "My2019AppleID" into the password field on the AppleTV, get a Verification Code (say you received "123456") and append that to the password, so your password would read "My2019AppleID123456" before you clicked "Enter."