adding verification code when I"m already in GMAIL.

I"m setting up active gmail accounts on new iphone. I added my first gmail account, got a verification code and got a prompt to enter code and did so. Then I tried to add the second gmail account, and got a verification code, but there is NO SCREEN asking for my verification code. Tried it several times. Then got an email on my phone about suspicious activity from my second gmail account. How can I enter verification code for second account when I'm using my phone and no screen is coming up asking for my code? Thanks.