Sorry, I re-read what you wrote and see that it IS global. Documenting my steps to potentially help out others…
In the Dashboard editor I found footer.php and could see that there’s a call to wp_footer(). Header.php contains a called to wp_head().
Now the comment.php file… I had to go to the file manager of my web host to look for this, as it’s not available from the WP Dashboard. I realize that the php file edited yesterday was NOT the comment.php file. That one was called wp-comments-post.php and was in my public_html directory.
I found comment.php in the wp-admin folder… but there are a whole bunch of switches relating to comment editing and moderation and nothing about any input fields. So I haven’t a clue about where to put the lines of code I’m supposed to insert.
Then I found ANOTHER comment.php file in the wp-includes folder. But I can’t find input fields there, either.
Then I went looking down in the Theme folder (where I found header.php and footer.php), but no comment.php.
I found comments.php in a subfolder of the wp-includes folder, and it has a coded comment that the file is there for backwards compatibility. When I edited that, the “Connect with Facebook” button appeared!
It still doesn’t seem to work the way I’d expect, though. The button is there, it asks for my Facebook password, etc., but then I still have to fill out the name and e-mail fields… and it doesn’t seem to actually connect to Facebook.