4wd is typically engaged via an electromagnetic clutch. So first thing I'd do is to disconnect the connector that the shift motor is connected to (which is the same connector that the electromagnetic clutch is connected to). This will throw a 4HI/4LO blinkng light on the dash (and maybe a non-working speedometer) but since were just diagnosing the problem, then that stuff doesnt matter. Anyways, go around the neighborhood and see if the sound still exists. If it goes away, then the problem is electrical. If it doesnt, then the problem is mechanical and is "downstream" (in terms of power transmission) of the electromagnetic clutch. A "BFH" probably wont work int this situation, especially not on the shift motor since the shift motor only controls HI/LO range, not 4wd.
So if the problem still persists with the connector unplugged, then plug it back in and remove the front driveshaft. Go for that same drive. If the sound doesnt goes away, then its downstream of the driveshaft and is something related to the front axle. If it goes away, then the problem is probably internal of the transfer-case.