I use gmail from a browser and as mentioned above signing out seems to work for me. I most often though use the browser's Private Mode (or incognito mode or whatever it's called on your browser) which is a separate browser session which does not see the main session's cookies. When all private browser windows are closed all browser data is cleared. On re-opening the private mode I have to sign in again.
I would expect (I am not an expert though) that deleting the browser cookies should also sign you out. Browser History is something specific and is unrelated to cookies. It is a list of the most recent pages (possibly all pages) that you have visited. I think I recently tried deleting all the google related cookies that I could see and that did successfully persuade the browser to forget my gmail sign in.
If you delete all the cookies you will lose all saved sign in data. Make sure that this will not excessively inconvenience you.