Back in the day before they were power outlets, when they were just cigarette lighters, they were thinner in diameter than today’s 12 volt power outlets. Hold your cigarette lighter next to the GPS plug, and I bet the GPS plug is wider.
If I am right, I recommend you get an adapter, like an extension cord or one that lets you plug more than one device into the lighter. If the male end of the adapter/cord is narrow enough, it might fit into the lighter, allowing you to plug the GPS into the female end.