Sign out of chrome but use gmail

Chrome 83:

Go to ⋮ > Settings > You and Google > Sync and Google services
and disable Allow Chrome sign-in.

Chrome 70:

Go to ⋮ > Settings > Advanced > Privacy and security
and disable Allow Chrome sign-in.

Allow Chrome sign-in
By turning this off, you can sign in to Google sites like Gmail without signing in to Chrome

Now, when you sign in Gmail, it won't sign in Chrome.

After so much wasted time, I found the answer in this blog post:

https://news.softpedia.com/news/how-to-disable-the-auto-sign-in-feature-in-google-chrome-69-522856.shtml

Navigate to chrome://flags/#account-consistency and switch the Identity consistency between browser and cookie jar flag to "Disabled". Relaunch chrome - and you're set.