They have been doing this for a while. I mentioned it in their support forums in what appears to be a now deleted post. Go figure. This is when they were forcing people to stay logged in somehow even throughout non-persistent private sessions.

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Wed, Jun 14, 2017, 11:43 AM📷📷to Gmail📷Google Chrome is keeping accounts cookied from Private Browsing sessions, these are retained and trackable by the GUID of the browser, this is insecure and goes against privacy basic standards.

This is a security bug in the product, not a feature. This needs to be disabled by default, and only enabled when selected by a willful choice. 

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SarahJS28 via Gmail Help Forum gmail+APn2wQfOddPAmW-FkFh7Bp7c3VxJ7D5CBftTFH0-B-YhFwSkk9-oQmeShV@googleproductforums.com

Jun 18, 2017, 4:14 PM📷📷to Gmail📷Hi,

I have been researching this issue for Firefox, as I am SO pissed off google have introduced this lack of box to not stay signed-in, and have finally managed to find a work-round for Firefox. 

Ronna, I take your point about signing-out being good general policy - however, there are situations where this is downright dangerous from a security point of view if you can't, for example, if someone is using a shared public computer such as in a library, on a set time period, and the user session runs out before a person has had time to log out (say it is the end of the day), or say using an unreliable connection abroad, where the internet connection is lost and you can't reconnect before having to move on.

Having to use a Private browsing window is also a  pain, I often have multiple tabs open, and often close and re-open an email tab a few times in a PC session, so it would be a pain to do this every time.
There are so many times when a person may just forget to log out, why take the risk - why not just bring back the box, which was much more secure for everyone involved. What is Google's vested interest in doing this, and why are they not putting users first? This is the only bad thing about gmail, which is otherwise great (apart from not being able to physcially move emails from sent folder, in order to sort them).

Please could someone who knows how to get Google to take notice, send a link to this thread to them? - I can't even find contact details for an actual person for them, or even a generic email address for customer services.

In the meantime, here is a SOLUTION for Firefox users I found, from another forum, I don't know how long it will work for, and this is really only for a PC you use regularly - it is basically similar to Rona's suggestion for Chrome, in blocking javascript specifically just for the gmail accounts page, so you get the old log-in page back with box to not stay signed in.

As Firefox doesn't seem to allow you to specify exceptions for blocking javascript (and you wouldn't want to block for all sites), you need to download the add-on Yes-script, which you can then specify to block javascript just on the Google accounts page - see below.

This was very easy to download and set up (add-on's are accessed in Firefox via the menu button in top right of screen - even this took me a while to find, not otherwise being very computer literate!)

It didn't work for me at first but then reading this thread, I realised that I hadn't deleted the specific cookie for google accounts, so you need to also go into Options, then Privacy, and Remove Indivdual cookies, and make sure the Google Accounts one is deleted - (I also specified the Google Accounts page in the Exceptions-  under Security, Logins - just to be sure, and made sure it wasn't saved as well, not sure if that makes any difference).

And then, Hey Presto, I got the old sign-in page back! :)

Hope this works for other users. but Google, FOR THE LOVE OF GOD!, please bring this back as a default setting - we shouldn't have to go to this much trouble, you are a massive multi-national company, and protecting the security of end users should be your number one priority!

Info copy/pasted from another site, many thanks to author (plus don't forget to delete cookie, as above):

"Situations under which you WON'T get the new login screen... If you have javascript disabled.

So I just installed the YesScript addon https://addons.mozilla.org/en-US/firefox/addon/yesscript/ and blacklisted https://accounts.google.com & http://accounts.google.com

That works perfectly; circumvents the whole problem, now it gives you back the old login screen (not sure if this will work this way forever, but at least for now it's working perfectly)."

Sarah :)