Chandelier Repair

GDCS* electrical fixtures. Tried to change a burned out light bulb in the dining room chandelier and the ignorant socket starts coming loose. Hang fire and tarnation. So I push the table out the way, climb up the ladder, disconnect the wires, unscrew the bracket from the ceiling and set the fixture down on the table. Now I can open up center section, expose the rats nest of wire and feed the wires through the support arm so I can move the socket out of the way so I can see what the problem is.
    See the little white square with the small hole in the middle, sitting in the dark recess of the brass shell? The white square is one end of a little bracket. The other end has a bigger hole and screws onto the end of the support arm. The bulb was stuck in the socket, so when I tried to loosen it, instead of the bulb coming loose from the socket, the socket tried to unscrew from the arm. Tightening the screw that goes in through the bottom of the socket would have also tightened this bracket onto the arm. If I had know that, or just tried it, I wouldn't have had to go through all these shenanigans. But then we wouldn't have this picture.

*Gawd Blessed Chicken Excrement