Few possibilities.
Warn contactor in the axle.
Broken wire/wires to the housing
Bad switch
Broken wires are the most common problem.
There's a plunger inside the housing that gets released and break ground when the locker engages. Sending the signal to the light that things are in.
It is cosmetic, and for your info only. The locker, and operation of are 100% mechanical otherwise.
As in, as long as both tires turn, its working, regardless of what the light tells you.
I tore my wires off and repaired them several times before I finally gave up and just left them off. My lights where flashing for 2 years


If both tires arent turning, there's other problems. Come back then, and I can help you find that as well.
hth