Snoman may have thrown you off course. The ground is NOT switched. Here's
what the manual says:
First, check for a blown fuse (A/C-HTR fuse)
2) With ignition switch in run position, check for battery voltage at the
transfer case switch, terminal 1. If missing check for open wire.
3) With ignition switch in run position and 4WD control in 4WD engaged
position, battery voltage should be present at terminal 2 of the transfer
case switch. IF not replace transfer case switch.
4) With ignition switch in run position and 4WD control in 4WD engaged
Battery voltage should be present measuring between connector 3 and ground
at front axle solenoid. (That should be the actuator.)
Battery voltage should be present at connector between 3 and 4. If not
repair wiring. (4 must be the ground, and it's not switched!)
5) If step 4 is OK, disconnect solenoid harness, remove solenoid from axle.
Plug solenoid into harness. (Ignition switch in run position and 4WD control
in 4WD engaged) Solenoid plunger should extend within several seconds. If
6) Repair as necessary. :)
If I were you, I'd use a test lamp and not a digital meter.