I’d been trying to set up two-factor authentication for my Apple ID for a while but I was getting the “…not available for your Apple ID at this time” message. All of my devices were up to date and I could set up two two-step verification but I wanted the more up to date two-factor version. This lasted months and I couldn’t find a solution anywhere.
I happened to be looking through my iCloud preferences on my iMac and I noticed that my “Primary” email address had not been verified. Once verified – woot! – I could go on to set up two-factor authentication. I hope this might help someone who’s been pulling their hair out over finding a solution.