This is sometimes possible for a regular button (or indeed, a single
menuitem). Often these items have a very simple action, and if you are
lucky the action is delegated to another element, called a command or
broadcaster. Therefore all you need to is to create your own custom
button and designate the same command/broadcaster and that will often be
all you need to clone the behaviour.
However I don't think this is possible for more complex objects like the
URL bar. Instead what you could consider is to change the styling of the
existing elements in full screen mode. (This includes overriding the
hiding of the navigation toolbar in full screen mode.) It might even be
possible to do this entirely in CSS.