Everyone please pause for a moment. There is a lot of misinformation in this thread.
The indicator lights on the dash exist for the following: Part time 4WD (high range mechanical connection - do not use on dry pavement), Full-time 4WD (high range, differential coupling, can be used on all pavement), and 4-LO (Low-range mechanical connection - do not use on pavement)
Neutral and 2WD positions do not have any indicator light.
The selector handle is THE ONLY TRUE INDICATOR of the position of the shift forks. It is connected via a cable to the shift lever on the body of the transfer case.
The light is generated via a plunger switch that is inside the top of the transfer case. This plunger is pressed in by the lever as it moves from place to place, and the farthest-extended position is the 2WD location where the switch should be OFF.
If you have been driving with the selector handle in "Full-time 4WD" (two pulls back from 2WD) and you have no dash indicator... THE DASH INDICATOR IS WRONG. The plunger switch has gotten out of alignment (this happens quite easily) and / or the switch has failed entirely.
From what I understand, the switch is not protected from contamination - another brilliant design choice - and gets full of crap that causes it to jam or fail out. You may be able to access the switch from above, as that other thread should be describing. The main thing to remember: The dash indicator MEANS NOTHING to the engine / car / computer / transmission / or anything else. It is ONLY there to tell you what you have done with your hand lever... IF you are incapable of simply looking down to see it.
Best of luck with that switch. I never replaced mine when it acted exactly the same as yours... Because one day it just fixed itself. It did it again a year or so later... And again fixed itself. Cheap chinese component, probably.