An easy way to test these light PCB's out of the game is a 9v battery and a couple of alligator clips.

The sockets do go bad. They can lose tension on the bulb or break all together. Or the 2 arms don't quite make full contact with the PCB. You can try bending them downward slightly. Also you can and should refresh the connection point between the lamp socket and the PCB. Do you see those little dots/impressions in the crescent areas on board? Take your soldering pencil and reheat those areas. You can add a tiny bit of solder to the area, just make sure you keep things level and even. Those indentations can cause bad connections as well. The last point of failure is bad/cold solder joints on the connector itself. Reheat each pin with a little fresh solder to make sure those are good to go.

As to your proposed fix, yes that would work but I would check everything else first.