Gibson CS336 grounding problem...

Does the hum go away when you touch the strings? Or only when you touch the cord plug? Or the pickup covers? Or the ring around the selector switch?

If it's a broken or reversed ground connection, some of those should stop the hum and one (or more) might not, which will pinpoint where it is.

 

Sounds like the ground connection is bad between the jack and the switch - assuming 'traditional' Gibson wiring where the cable from the jack goes directly to the switch, not to a connector inside the control area.

It could be that the inside of the barrel itself is dirty or corroded - try cleaning it with a little fine sandpaper wrapped around a screwdriver.

Has the jack been disturbed or tightened? It's possible that the ground wire has come off.

Another possibility is that the barrel of the socket is making a poor connection with the flat ring with the tab that the wire is soldered to. They sometimes do this if they're left for a while and the metal corrodes, but it's unusual on a fairly new instrument. If it is this, you can fix it by carefully soldering the barrel to the ring... or just replace the jack.