On this vintage Jeep, there is a vacuum disconnect on the front axle. In 2WD, the right axle shaft is disconnnected, allowing the front to partially freewheel. When the transfer case is shifted into 4WD, a vacuum switch in the transfer case engages the right front axle shaft. You can be "in 4WD" as far as the transfer case is concerned, with without that axle engagement, it isn't actually getting to the wheels. So as DDC XJ notes, your first job is to determine that you are really getting 4WD at the wheels. Loose or rotten vacuum lines, a poor vacuum switch at the transfer case, or a bad vacuum motor on the axle, can all prevent it from working right.
Assuming that the 4WD is truly engaging (that is, the vacuum motor on the axle is engaging the axle), the indicator light is powered by a vacuum switch located somewhere on the right inner fender, which is fed by the vacuum motor on the axle. Check that the vacuum line from the axle shift motor is connected, and that the vacuum switch is working.
The first thing, though, is to be sure that the axle is really being engaged.