Did this problem just start or has it been like that since you bought the vehicle? .... or maybe after work was done on the diff?
I ask because if you can hear the motor then you don't have an electrical problem ... it will be mechanical. Here I see one of two probabilities .... if it's just started then it's possible that the worm gear is stripped, .... if it's always been like that since you had it or after someone has worked on it, then it's possibly the above by co-incidence or the actuator is not engaging the diff lock 'fork' in the diff.
Either way, you would have to disconnect and remove the actuator motor, clean and inspect it. Sometimes the problem is nothing more than an accumulation of muck inside.
Best of luck that it's nothing serious.