Micha I don't want the footer link to go back to the top of the page
I want the footer link when clicked to act exactly like this link
As someone who has done some fairly extensive modifications to the script for a site that needed some fairly heavy customization - I can tell you that certain functions aren't as easy as they look.
If you look at the way that I modified the theme on worldofbb.com, I wound up replicating the functionality that you're looking for by making the button on the bottom work exactly the same way it does at the top. That's because that button is built using a conditional statement, so it isn't a static link.
The conditional statement is located in the file themes\default\subtemplates\subnavigation_1.inc.tpl
(The forum spam filter won't let me post the relevant code. It's the code in lines 11 through 13)
I used this code as the basis of my footer link. Mine has a bit more code in it because I've made other modifications to the script above and beyond modifying the theme - but the basic concept remains the same: You would need to use this code to also form the link in the footer if you want it to work consistently. That means the link can't ALWAYS be a "Back to the forum index" button for the simple reason that the link "/forum/index.php?mode=index" is actually not always going to perform the same function at all times. Depending on the page you are on it will perform different actions, which is why the link is not always offered on all pages.
Now, having said that - off the top of my head I can't think of a specific page where using that link SHOULD cause you to logout - but I do know I specifically had some issues where I had to make some modifications to the way the 'back' links worked when someone visited the register and login pages. There were various situations where I would run into login issues if the exact wrong sequence was followed which required me to use some workarounds to avoid them - but it was a while ago so I don't remember specifics.
But honestly, the easiest way to resolve it is to make the link work the same way in both places.