All the indicator means is that the ecu is grounding the proper circuit to power the coil in the dif. Notice that the indicator will not be on in neutral. It also won't come on if you're driving over 3000 rpms and you flip the switch but will once the rpms come down. All it's saying is that conditions for engagement have been met and the circuit can be powered. It's not saying that it's working. You could have a bad coil, relay, or breaker. The Armature could be bent or you could have a bad ground. I'm sure there are a bunch more reasons that could cause this. The first thing I'd do is ensure that the coil is getting 12 volts when the key is on, AWD is switched on and the trans in a gear. Make sure the wire isn't broke where it enters the case, it's kind of a weak spot if you ask me. All of that is thinking the issue is electrical. I had a link to a manual for the Hilliard but the link doesn't work anymore. There are manuals available online if you do a search for Hilliard drive manuals.
On the mechanical side maybe the cage is broke, I don't know why it would be though. Maybe a couple of flat H-springs? Mechanically there just isn't a lot to wrong with these things. Good luck man