It sounds to me, just like you said, it could be a ground problem. This can be caused by a loose/bad connection in the grounding. Since your guitar is fairly old this is a good possibility. Also contributing to the sound could be bad shielding. Older guitars had poor shielding becuase manufacturers didn't know the importance of it. The only way to be sure is if you open her up. The noise that you experience when you have the humbuckers tapped in single coil mode is going to happen no matter what. Unless you wire it to activate the whole humbucker but only transmit the sound from the coil that you want. That can be done with a kill switch wired to the coils you would "knock out". But since your priority is to figure out why your guitar makes this annoying noise, I suggest taking it to a shop unless you feel comfortable using a multimeter (voltmeter) and working with a soldering iron. If you do feel comfortable you can simply open up the guitar and check all the connections throughout the guitar. Check for fluctuation in the read out. Also it might be a good idea to wait until the guitar acts up again to take it apart. That way, if it is a loose/bad connection, you should be able to spot a little easier. Hope you get it figured out. Good luck!