Just the odometer or the speedometer as well?
1996 will use an all electronic speedometer/odometer and an electronic overdrive.
This requires a speed signal from the VSS(vehicle speed sensor) located in the old speedometer cable hole in the trans or transfer case.
Check its wiring connector, and pull it out of trans to check its gear.
Good read here: Ford Ranger Speedometers - How They Work
You might also check inside fuse panel, I don't have a '96 diagram for fuses but it could just be a fuse blew