Gmail asking for authentification Pop-up window supposed to open Safari does not work.

Hey there Lost-in-Eiffel-Tower,

Thanks for reaching out to Apple Support Communities. Does it work if you try authenticating using a different browser? What if you restart your Mac? 

If not, you may be able to find a way to resolve this using the steps from this link:

2-Step Verification - Google Account Help

We hope this helps. Take care.

But if Firefox is open, when you click on that authentication dialog, it will send a string into Firefox and the Gmail sign-in page will accept your name and password. Once done, you have Gmail authentication satisfied in Apple Mail. It ignores the default browser when it is Safari, but when I tried the previous sentence, it worked fine with Firefox. Go figure…