I used a second Gmail email account on Apple TV in the past fine. But I used a second account. I realized, I wanted all my YouTube to happen on my main Gmail account. So I signed out on Apple TV and signed in with my other active gmail account. But after entering the correct password, it said it was wrong.
So I went to gmail and youtube on my iMac and, it worked fine. But I changed the password just in case (resetting it). Again, Apple TV said it was wrong.
After repeating the password over and over with that horrible hand cramping little aluminum remote, I came to this posting. Created a channel with a new name (instead of the gmail address) which, is a total pain the rear and not at all easy to figure out or do.
Then I entered the new channel name instead of my email plus the password I had tried before and it logged me right in.
So this is a FLAW in Apple TV!
Having trouble logging in to YouTube? Create a channel (user name) and log in with that.
Ironically, I used to have a YouTube user name but when Gmail bought it, I lost it. Now, of course, no sane sounding user names are left.