If you want to get rid of the hum then you have to take action.
- Try the connection with/without the ground connection and report the results.
- The ground wire needs to be connected to a solder lug on a screw terminal under the back right top plate that you can remove by pulling the wood trim forward.
- From that same lug, there should be a connection to the black multi-pin connector.
Please see the excellent video by Beolover