10 minutes is more than enough to start with. After doing it for awhile, you'll find yourself wanting to increase that time, but just do it gradually.. maybe work yourself up to 20 minutes, but if you ever feel like you don't have the time, just make sure you're doing at least 10 minutes.
Well, Google TFA doesn't ask you to type your number (and others only some digits) so it probably would rise a red flag big enough to "awake you" from auto-pilot, I hope.
I assume you're using the type of 2FA where this is not the case. We are discussing the type of 2FA where Google does ask you to enter your number. I.e, TOTP. When I log into Google, it asks me to type my 2FA number in.