I have a 1992-1996 Ford PSOM (Instrument Cluster) and my speedometer isn't working and/or transmission isn't shifting properly.

The VSS is known to fail especially since this is an aging vehicle, you must inspect and replace the (vehicle speed sensor) with an OEM MotorCraft one. 
When one of the systems that work together fails or is intermittent, your vehicle might experience hard shifts, the speedometer doesn't work, or both. It's quite unusual that the shifting gets affected by a faulty VSS or PSOM however, it's very much possible with these specific vehicles. That's also not to say a hard shift couldn't be caused by something else. 
The VSS signal goes to the RABS (Rear Analog Braking System) control module before it continues going to the PSOM (instrument Cluster), The output of that goes to the computer PCM (Powertrain Control Module) and Speed Control module.
It's a process of elimination when it comes to the transmission hard shift and/or speedometer not working correctly. Try unplugging the Speed Control module for a while, and see if the hard shifts go away. If not, plug it back in then do the same with the RABS module (located behind the glove box).
The PSOM (Instrument Cluster) is commonly known to fail and you can have peace of mind knowing that when this comes in for repair, we address the circuit issues that may cause these issues to occur.
 
Below is a list of 1992-1996 Ford Vehicles that are affected:
  • Ford F150
  • Ford F250
  • Ford F350
  • Ford E150
  • Ford E250
  • Ford E350
  • Ford Econoline
  • Ford Bronco