When testing a 4WD solenoid, you will need a few tools. A multimeter will be needed to test the voltage and continuity of the solenoid. You will also need a 12-volt test light or power supply.
First, you will want to disconnect the battery negative terminal to prevent any accidental shorts. Next, locate the 4WD solenoid on the transfer case. The 4WD solenoid should have two wires going to it, one with a black/white stripe and one with a solid black wire.
Using your multimeter, first test the voltage at the solenoid terminals while someone is depressing the brake pedal (this engages the 4WD). The voltage should read around 12 volts. If it does not, then there may be an issue with the fuse or relay for the 4WD system.
Next, check for continuity between the two terminals on the solenoid while someone is depressing the brake pedal. There should be continuity when engaged and no continuity when disengaged. If there is no continuity when engaged, then this indicates that there is an open circuit somewhere in either of the wires going to or from this solenoid.