My 4 wheel drive selection switch lite does not work. Does the 4 wheel drive system still work properly?, or is it an indication that something is wrong?

The reason the light is flashing constantly is because the vehicle is sensing that four wheel drive(4WD) is not working. These 4WD systems use vacuum from the engine to engage/disengage to front axle. The vehicle probably has no vacuum going to the front axle, which would not allow the 4WD shift to complete, which would then leave the light on the dash flashing.
First thing to check is that the vacuum actuator on the firewall is working as it should.

Which of these does your vehicle have ?

Transfer Case - NVG 233-NP1 (Two Speed Selectable)
Transfer Case - NVG 136-NP4(One Speed Automatic)

The New Venture Gear NV233 is an electronic shift transfer, with the following three modes of operation, Two-wheel drive high range, Four-wheel drive high range, Four-wheel drive low range. The gear reduction for low range is provided by a planetary gear set. The floor-mounted shifter has been eliminated. A switch, located on the upper right side of the instrument panel, is used to select the operating range. The indicator lamps on the switch show the current mode of operation. When the four-wheel drive has been selected, the four-wheel drive indicator lamp on the switch is designed to turn on when the front axle has engaged.


Automatic Transfer Case
The single speed automatic transfer case system shifts automatically from rear wheel drive to four wheel drive when the transfer case shift control module (TCSCM) senses the difference in rotation speed of the front propeller shaft and the rear propeller shaft . Two vehicle speed sensors, one located at the rear output shaft area of the transfer case, and the other, located at the front output shaft area of the transfer case, send front and rear propeller shaft rotation speed information to the TCSCM.
When the front and rear output shaft rotations remain the same, the TCSCM sends pulse width modulation signals to the encoder/motor to keep the transfer case in rear wheel drive. When the front and rear output shafts rotations are different, the shift control module sends pulse width modulation signals to the encoder/motor to engage the transfer case into four wheel drive.
The system will automatically transfer a percentage of torque to either the front or rear axles as required to stop all wheel slip. When the front and rear output shafts rotations return to the same speed rotation, the shift control module sends pulse width modulation signals to the encoder/motor to position the transfer case back into rear wheel drive.
When the transfer case is engaged into four wheel drive, a lamp indicator on the instrument cluster will light. The automatic transfer case system is completely automated, no transfer case control button switching system is required.

Do you know what diagnostic trouble code's are ?

DTC C0300 Rear Speed Sensor Malfunction
DTC C0305 Front Speed Sensor Malfunction
DTC C0308 Motor A/B Circuit Low
DTC C0309 Motor A/B Circuit High
DTC C0310 Motor A/B Circuit Open
DTC C0315 Motor Ground Circuit Open
DTC C0374 General System Malfunction
DTC C0376 Front/Rear Shaft Speed Mismatch
DTC C0550 ECU Malfunction
DTC C0611 VIN Information Error
DTC C0895 Device Voltage Malfunction

Not OBD2 engine code's .

AWD Disable indicator
The AWD Disable indicator is located in the instrument panel cluster. This lamp is used to inform the driver that the AWD system has been disabled and no torque will be applied to the rear wheels during a slip condition. The AWD Disable indicator is controlled by the powertrain control module via a class 2 message.
Powertrain Control Module
The powertrain control module monitors the data from the ABS controller and Rear Drive Module (RDM) for proper operating conditions. If inappropriate conditions are present the PCM commands the differential clutch pump actuator check valve closed, disabling the AWD system. The PCM also commands the AWD Disable indicator on.
Is the All-Wheel Drive Disabled Indicator Always On ?

Is

To Troubleshoot Transfercase stuck in 4wd issue.Click the link below and follow the details:
http://www.allcarhelp.com/2015/04/transfer-case-stuck-in-4-wheel-drive.html

This will help.
Thanks.

Something you can do is to tap the 4/4 motor under drivers side on the back of transfer case with key on engine off. Have someone work the buttons as you gently tap the motor. Don't hit so hard as to dent it. Usually works.

I was researching the recalls for the 2002 tundra and havent found any recall pertaining to the 4whl drive. Sometimes when people have their 4wheel drive locked in and drive on pavement for any length of time, whether it be just a couple of feet or a couple of miles, over time it creates a binding of the gears in your transfer case. Once the bind is so great, the engaging and disengaging starts malfunctioning and leads to bigger problems overall. I could be wrong about this being the problem that you have but I think its something to look into. It wouldnt hurt to put your vehicle up off all fours and release the bind if any by running through the gears while in 2 and rour wheel drive while all four tires can move freely and release. See if that works for you. Check your gear oil front , center and rear and use much caution when attempting this suggestion. Also refer to your owners manual troubleshooting section for other possibilities. Merry Christmas. By the way, the electrical switch should be covered in the troubleshooting section also.

Your dash lites are on with headlamps off? I'd check the wiring for headlamp switch/dimmer. Not only check the fuses, check the fuse circuit for voltage, use a test lite. You could use a jumper to bypass dimmer, see if dash lites work.

Do you have it switched to 4 wheel low? If not it indicates a problem with the 4 wheel drive sustem. Take it to a mechanic for proper diagnosis.

Hi, You will need to take to mitsubishi dealer and have them scan your diagnostics. But this is a common thing in montero's and it sounds like o ring (which is plastic) in transfer case has busted. As long as it switches in and out of 4 wheel drive it is ok to drive. If it doesn't, dont drive it...it could cause alot of damage.

sort of switch