If the adhesive is still tacky, I usually start with Gorilla Tape, which is a heavy duty duct tape with extra strong adhesive.
I tear off a few inches of tape, press it onto whatever I'm trying to remove, and then pull it off, repeatedly, while moving around to fresh areas of adhesive on the tape. Usually the old adhesive will prefer to stick to the Gorilla Tape.
If that doesn't work, *then* it's time for the line-up of increasingly aggressive solvents.
I would be careful with Goof-Off, however. It's great on bare metal and some surfaces, but I had it go right through the insulation on a ribbon cable trying to do exactly what you're attempting. Oops.