Entering verification code.
I need to enter a verification code on my older Mac. The screen never pops up to enter it. I am getting the code but can't input it.
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See if the information in this paragraph from the Apple two-factor authentication article helps. You didn't say what model iMac you have or the version of macOS it is running, however on older OS version it says the verification code gets entered as part of the password. Hopefully that will resolve the issue.
Two-factor authentication for Apple ID - Apple Support
What if I use two-factor authentication on a device running older software?
If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field.