Sometimes bassists have used string muting to get a particular sound. I can't think of anyone that did it with a Stingray but McCartney did it with a Ric on songs like Glass Onion. It kills the sustain and the note doesn't ring like it does unmuted.
I tried it once on a southern gospel session. I did it with styrofome (<-is that how you spell it?) Anyways, I placed it in front of the bridge on a late 70's stingray 4.