The power divider on a civilian tandem axle truck is an integral part of the front differential. If you have one, it will be obvious as a large extra casting on the front diff. It does not disconnect one of the axles, but has its own differential in it that allows one of the rear axles to turn at a different rate of speed than the other while still transmitting power to it. This allows for differences in tire diameter, etc. This prevents the tire scuffing and axle windup normal military trucks get in the tandems because both military truck axles are locked together by means of common design differentials with a common driveshaft transmitting power to both. There is no provision for one axle to turn at a different rate than the other. When the differential lock engage lever is set, it locks the differential in the power divider so the axles have to turn together like the military configuration. All of the power divider lock switches I have seen warn you to not use them on dry roads because of tire wear and axle windup, which is precisely what you get with the locked military axle design. I have an M135 deuce I use on road loaded a lot, and we put a civilian tandem set under it with power divider to get away from the locked axle problem. I have also machined dog clutches to put in the driveshaft to the rear differential so it can be readily disconnected for road travel. When my M543 A2 wrecker is in normal use where six wheel drive will not be needed, I simply pull out one of the axle shafts and replace it with the cap cut off another old unused axle. This frees up one axle as a free-roller and the other drives the truck. No damage can occur to inside diff parts because all are turning in a normal manner. If the truck is to go into the goo, I replace the axle shaft. Using an air wrench, it only takes a few minutes to switch. When I get time, I will make a clutch for it, or other means of controlling the drive to one axle. It is amazing how much more freely the truck will run down the road when the drivetrain windup is not happening. You will also see tire life increase dramatically.
If you wonder about your dog clutch in the front, jack up one front wheel. With air up and the truck shut off, put it in any forward gear and try to rotate the jacked up wheel in both directions. It should turn freely one way and lock up the other. Put the shifter in reverse, and try the same test. The event should happen in the opposite rotational direction. You can also test the switch you are wondering about the same way. If you do not get the lockups, the sprag is bad, the air cylinder that operates it is not working, or the air supply is not getting to it. Regards Marti