Umm....
Create the brush, tie it to an entity (I believe funcbrush should work pretty well for this).
Then create a logicauto, open it's settings, go to the outputs tab and create something like this:
My Output Named: OnNewgame
Target Entities Named: nameofyourfunc_brush
Via this Input: Kill
After a delay in seconds oft: 4
I haven't used the "Kill" output before so I'm not 100% sure that it will do the trick...
The one with a button would be basically the same, but instead of a logicauto you would use a funcbuton (obviously), and the output (from the button) would be something like this:
My Output Named: OnPressed
Target Entities Named: nameofyourfunc_brush
Via this Input: Kill