I purchased a used ‘04 Liberty Limited and ever since I’ve it the part-time light is always “ON” when the transmission is in 2Hi and if I shift it to 4Hi the light would go out. I believe it should be the other way around and not sure what is causing the problem. Occasionally when driving on the hwy in 2Hi the light would go out by it self, but eventually it would come back on again. So far I was able to determine that the rear wheels are engaged and the front are free rolling when I jack tested. I suspect it maybe a sensor or switch issue. Any suggestions to fix this problem would be appreciated.

 

Check the adjustment of the shift linkage.

 

There also is an electrical transfer case position indicator that is responsible for the connection and light.
It is located at the top of transfer case and can cause this problem, if all is well in the linkage department.