Generator by size. Brosol bigger than standard solex so I get that the carb is a Brosol 30/31PICT instead of a native solex 34. It has the idle air adjustment that is on the later solex carbs plus an extra vacuum fitting. Should have blown the pictures up bigger

Carb and intake manifold will need a cleaning, soak in Simply Green, as they are surely filled with fine dirt/sand. Also if you are real careful with the manifold taking it off, maybe loosen the head ends and stuff rags into the holes, you can avoid getting dirt into the heads/cylinders. Alternately pull the rockers so the valves will all fully close and then blow out the intake ports with compressed air. Although since you live in a desert area you probably have your own process for taking care of fine dirt that gets into everything.