Thanks also, Commanche and Collinba; I also did as per your recoms.
First I disassembled the handlebar throttle controls and sprayed everything with a cleaner; then I used light oil to penetrate the cables at the same time turning the throttle in and out. After the fluids seeped in, I was still hearing the squeak so I sprayed a cleaner where the cables went into the fuel system. Squeak gone!
After assembly, I adjusted to a handlebar point where the grip returns with no effort. There is a handlebar spot where it doesn't return. Then I adjusted cables for tension and free play. Locked the nut.
Started the engine. Squeak gone; grip doesn't stick. Perfect!