I know similar questions have been asked but none those I found involved the same situation.
So here is my situation: I have two gmail accounts. The first is always opened on my computer, that's where I get reminders for my agenda, urgent mails that need a quick answer, etc. The second one is only for things that I want to keep on a long duration (like my bank's mails or similar stuff). I have my own reasons for using two account and not just making two files on the first one. As you may know, you can't (or at least it is hard to) open two gmail sessions on the same computer at the same time, so what I usually do is opening a private session or use an other internet navigator for the second account when I need it. I also have no smartphone (no android or anything else) and I don't want to give my phone number to google.
My problem is that sometimes Google blocks my second account because it doesn't recognize my device. So after I enter my adress and password I get a message that asks me to enter a phone number so they can check I am the right person. What can I do to avoid this?
I already tried to contact gmail's tech support, but they just refused to help me, telling me they couldn't let me access this account if they couldn't be sure I was the right person.
Currently I should have received a quite important mail on this adress, and waiting a few days is not an option. Ideally I would like to have a quick way of getting access to my mail right now and a long-term way of avoiding further occurences of that problem.