Had this same problem on my 96 ford thunderbird though started with turn signal blowing fuse. Didn't realize till later was also on my back up light fuse. Researched and found out back up function went thru neutral safety switch. Just before this problem had cat converter replaced- wondered ? When cat welded in they torched wires at neutral safety switch. Took back to them and pigtail at switch all melted together. They separated all wires and taped back together and fixed my problem. Not sure if this helps you but maybe problem within, wires or plug for neutral safety switch ?
Also back up light switch which is part of the park netural switch on the trans. linkage. If no power as gg said. Key on, wiggle shifter up/down a little and have someone looking at lights to see if they blink on.