How to space closet supports with even number of 16" spaced studs?
In my house the closets have 1x4 screwed on top of the sheetrock, on all 4 sides (minus the door opening of course) to mount the brackets. The shelf and rod bracket is exactly the one you have pictured. Where it is attached they added a short 1x4 vertically (with rounded bottom corners actually) to make a level mounting surface.