I couldn't disable, but I did find this work-around solution, and it's working out fine:
Turn on Parental Controls and block access to any applications that auto-sign into the google account.
Parental Control is password protected and it allows me to have full control of the security features. I used it to turn off access to all kinds of things. But most importantly, on my tablet I could block access to all or some apps. I chose to block only the apps that gave access to gmail: the browser and the Gmail app. I can still access those blocked accounts using my Parental Control Password. It's clunky though. Once I unlock an app to access it, I actually have to go BACK to the security settings to re-block it. I thought maybe it would stay locked and continually let me sign in with my password, but no, each time I sign in & unlock it, it's permanently unlocked. Well, it's better than nothing... and since I plan to hand this tablet over to my kiddo I won't be needing to access gmail on that tablet, much, anyway.
Next, so my kiddo and her friends can still surf the web, I went to Google Play and downloaded a third party browser with decent reviews on Cnet... "Dolphin Browser". Dolphin Browser works great and does not have any auto -sign in popups.
Sometime during my research, I read about downloading Googles' "Chrome Browser" as an option. But couldn't make sense of the forum's discussion as to whether Chrome was still popping up an auto-sign in. I'd like to be able to stay in the Google family, but I guess they don't want me. :-* My tablet doesn't support Chrome, anyway, so I can't even give it a test-try. Luckily for me, the Dolphin is just fine.
The tablet still allows access to Google Play. We use a Google Play Card which we've already entered onto the gmail account (via a regular computer). To buy something off of Google Play, the user would still be able to access the "redeem" feature... There is a request for some kind of number though -- I can't tell if it's asking for the code # from the card? Or if it's asking for my Parental Control pin #. I'll let you know next time my kid needs to buy something off Google Play. Gee after we uploaded the card to Gmail, we prob threw it away so I hope it isn't asking for that card's code #.
Also, since my tablet was going to be used by kids and we'd be using it while traveling, I also made sure to use the basic security features on the tablet:
1) locked the screen with a password/pin or patter - (basic security just in case tablet gets lost)
2) typed in my contact email for the front, locked screen (in case an honest person finds the lost tablet)
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