When a bath vanity needed to be turned against an adjacent wall and the light needed to be removed from it’s location above that sink, I devised this method to patch the hole flush with the surrounding drywall.  There was a stud about 2 inches from the perimeter of the hole to be plugged.  I fashioned a circle of plywood 9 inches in diameter and centering it over the hole, drew the stud location.  I cut that off and cut the remaining partial circle into two halves that could be inserted into the hole.  Then I made an annular ring of 1/4″ plywood of 8 to 9 inches in diameter.  I matched this to the perimeter of the 9 inch plywood circle and cut and fastened it.  Then, with fingers crossed, I wetted the back and front of the drywall around the hole to a distance about 2 inches around the perimeter.  After inserting the pieces of plywood circle behind the drywall, I screwed through the ring to hold the plywood 1/4″ behind the drywall, added a 4 inch circle of drywall, then started several screws at about 3/4″ outside the hole perimeter, gradually advancing them all until the entire wet drywall perimeter was drawn into the hole depth. (Since doing this I’ve realized small cabinet screw heads are even better than drywall screws at holding the surface in). I allowed it all to dry.  Then a paper tape circle about  5-1/2″ round went in on a bed of mud and a filling coat over that.  Wallah!   A patch that was flush with the wall.