I have a 2001 Dodge 1500 ram 4X4, 5.9L, my OD light comes on at random times, while driving flat surfaces and at times when starting the vehicle. I can turn the OD light off and the truck drives fine. The OD still works also when pressing the button driving up hill. I have checked for codes and there are none, no indication of overheating on the transmission.
Any common issues out there?

 

The O/D Off switch simply sends a signal to the PCM. PCM controls the light. Wonder if the switch is going bad, or you have a short somewhere.

Welcome to DF! Moving this to Second Gen Ram section for ya.