This might be of interest to anyone with this combination of lens, camera and grip. It might well apply to other problems with battery grips, bodies and lenses as well.
My Sigma 500mm f4 Sport has proved very successful on both my D500 and D810 bodies. Very sharp, good focus and effective OS (VR in Nikon speak). It suddenly started doing strange things on the D500 the other day. Jumping in and out of focus, changing the focus mode settings autonomously and doing a strange clunking thing at the end of an AF period after releasing the AF-ON button on the body. It was fine on the D810 and so I decided that it must be something to do with the D500.
I downloaded the latest Firmware for the D500. No change. I updated the firmware on the Sigma. No change. I cleaned all the electrical contents on the D500 lens mount and the lens. No change.
Then I became suspicious of the battery grip. I have a Vertax battery grip on both cameras and I have never had any problem with them. The batteries in both camera and grip were fully charged and I swopped them over to double check. When I removed the grip, the problem went away, so it was definitely the grip. I then cleaned all the contacts between battery, body and the grip. I then replaced the grip, switched it all on and Bingo! All was well again.
I don't really understand why this happened but it may be that the Sigma is particularly sensitive to voltages supplied from the camera/grip and the contacts may have been mucky enough to lower these and to cause the problem. Interestingly, there were no problems on any of my other lenses, including two other Sigmas.