I had a 1990 Toyota Pickup. The lighter worked perfectly as a power port for accessories.
You should get a replacement cigarette lighter. Yours is damaged. If it was used for actually lighting cigarettes, the bottom of the lighter is probably corroded and will not make good contact with the GPS power cord. The cigarette lighter uses the sides of the positive, not the center, to power the heater element. the GPS power cord uses the center.
I had to replace my lighter on my 2000 Explorer because of this. When I bought it, the lighter worked, but no accessories would. Looking down the socket, you could see the corrosion and gunk build-up on the center button due to cigarette residue from someone actually using the lighter to light cigarettes. Replacing it was the easy option.