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I also do not have a stay in option.
In the preferences in google and I on the right site I have an option furthe google services.
There I disabled Allow iron sign-in and I am always signed in into ll google services.

I hope I can help. Because I have Iron in German and I tried to translate my German options into English.

Direct in Iron go to Settings -> You and Google -> Sync and Google Services

Now you see the topic Other Google services on the right

There you have to switch off the option:

Allow Iron sign-in

Then restart your browwer. When I now got to gmail and sign in I am always stay logged in even when I restart my system or Iron.