Matt,
The dash mounted temperature gauge uses a different sending unit than the dash mounted monitoring unit because the monitoring unit is reading information directly from the ECM (engine control module). An inoperative dash temperature gauge is usually caused by a poor connection or broken wire, and this is highly likely in you case because I think that the temperature gauge in the RR bay uses the same sending unit that your dash gauge does. However, there is a chance that the gauge itself is bad, but it does not fail near as often as the wires and connectors. The only way to determine the problem is just old fashion trouble shooting.
Gerald