Sometimes it's funny how something so simple can elude you for so long and then as soon as you see it, all you can think of is... "Why did it take me so long to think of that?!"
To turn your Grill Mount into a Wall Mount, all you need is a plastic thumbtack like the one shown in the photo. You don't have to match the color of your Grill Mount, in case you are wondering.
Step One: Push thumbtack into the wall.
Step Two: Hang your Grill Mount from the thumbtack.
Step Three: Start filming with you new Wall Mount.