05 f150 4x4. 4 wheel drive lights come on but it is not engaged?

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 .

You have a switch on the instrument panel ?
The NVG 263 transfer case features a three button shift control switch located on the instrument panel
The NVG 236/246 transfer case features a 4 button shift control switch located on the instrument panel.
Or
The New Venture Gear (NVG) 261, RPO NP2 transfer case is a two-speed, part-time with "mode shift-on-the-fly" capability. It has a chain driven front output shaft and an epicyclical low range planetary arrangement. The NVG 261 transfer case features a four position shift lever control located in the vehicle floor plan. As required, the operator can select 4HI position from 2HI "on-the-fly," as described in the owners manual. A dash 4WD lamp will continue flashing during shifting, until all criteria have been met and the new mode/range position has been reached. Once the new mode/range position is fully engaged and the front axle disconnect locks in, the dash light 4WD indicator lamp will remain ON constantly. Range shifting functions similarly, although it should be limited to speeds 8 km/h (5 mph) or less.

Check connection at the 4X4 control module , check power and grounds . Do you know how to do basic electrical testing ? Does your truck have manual or automatic trans mission ? Which transfer case does yours have ?

The NVG 263 transfer case features a three button shift control switch located on the instrument panel. When the ignition is in the RUN position, the transfer case shift control module (TCCM) starts monitoring the transfer case shift control switch to determine if the driver desires a new mode/gear position. At a single press of the transfer case shift control switch, the lamp of the new desired position begins flashing to inform the driver that the TCCM has received the request for a new mode/gear position. The lamp continues to flash until all shifting criteria has been met and the new mode/gear position has been engaged. Once the new mode/gear position is fully active, the switch indicator for the new position remains ON constantly. In the event that the TCCM can not or will not complete the shift, the indicator returns to the previously selected position; this is a Transfer Case Shift Control Switch Indicator Flashes, then Returns to Previous Mode condition.

The NVG 263 transfer case provides the driver with 4 manual mode/gear positions:
• 2HI - 2 Wheel Drive high range
• 4HI - 4 Wheel Drive high range
• 4LO - 4 Wheel Drive low range
• Neutral
Have it check for DTC'S - diagnostic trouble codes ?

DTC B0790
DTC B2725
DTC C0306
DTC C0327
DTC C0359
DTC C0379
DTC C0550

Your best bet would be take it to a qualified repair SHOP

It depends on what is wrong , is the 4x4 light flashing ? Are you aware of the complexity of the 4x4 system ? Has a electronic control module , has the ability to set an store DTC'S - diagnostic trouble codes !
Transfer Case The four wheel drive system is an electronic shift 4X4 system that allows the operator to choose between three different modes. The operator can switch 4X4 HIGH modes at any speed. To engage or disengage 4X4 LOW the vehicle speed must be less than 5 kph (3 mph), the brake depressed, and the transmission must be in NEUTRAL.
The shift motor sense plate, an integral part of the electronic shift motor, informs the generic electronic module (GEM) of the transfer case shift motor and contact plates A, B, C and D position.
The digital transmission range (TR) sensor is located on the LH side of the transmission, and informs the GEM when the transmission is in the NEUTRAL position.
The electronic shift motor is mounted externally at the rear of the transfer case. It drives a rotary cam which moves the mode fork and range fork within the transfer case between the 4X4 HIGH, 4X4 LOW and 2WD range positions.
When the GEM verifies the completion of the transfer case shift from 2WD to 4X4 HIGH (reading the contact plate positions), the GEM will then energize both pulse vacuum hublock (PVH) solenoids (supplying ground for 45 seconds). The PVH solenoid will allow a HIGH flow of intake manifold vacuum to the "wheel end hublocks", engaging the wheel end hubs to the front differential and transfer case to achieve four wheel drive.
Here are just a few DTC'S the system can set an store in the module !
P1804 4WD High Indicator Circuit Failure GEM GO to Pinpoint Test C . P1806 4WD High Indicator Short to Battery GEM GO to Pinpoint Test C . P1808 4WD Low Indicator Circuit Failure GEM GO to Pinpoint Test C . P1810 4WD Low Indicator Short to Power GEM GO to Pinpoint Test C . P1812 4WD Mode Select Switch Circuit Failure GEM GO to Pinpoint Test A . P1815 4WD Mode Select Switch Circuit Short to Ground GEM GO to Pinpoint Test A . P1820 Transfer Case CW Shift Relay Circuit - Failure GEM GO to Pinpoint Test A . P1822 Transfer Case CW Shift Relay Coil Short to Power GEM GO to Pinpoint Test A . P1824 4WD Electric Clutch Relay Circuit Failure GEM GO to Pinpoint Test A . P1826 4WD Low Clutch Relay Short to Power GEM GO to Pinpoint Test A . P1828 Transfer Case CCW Shift Relay Coil Circuit Failure GEM GO to Pinpoint Test A . P1830 Transfer Case CCW Shift Relay Coil Short to Battery GEM GO to Pinpoint Test A . P1838 Transfer Case Shift Motor Circuit Failure GEM GO to Pinpoint Test A . P1846 Transfer Case CONTACT PLATE "A" Circuit Failure GEM GO to Pinpoint Test A . Now are you sure you really want to mess with this ? You would need a factory diagnostic scan tool to check this out before you start replacing parts !
Here

2 speed electric shift transfer case problems #1 jack up truck place on 4 jack stands. Start and select 4 high position in drive release brake ad watch front driveshaft does it turn "yes" problem is axle actuator on passenger side of differential not engaging axle shaft. "no" apply brakes bring to a stop engage low range does low range work "yes" internal transfer case problems "no" electric transfer case shifting motor failure.

Without knowing how the 4X4 works you don't have much chance of finding the problem , (tapping on stuff ) ? There is an electronic control module that makes this system work . Could have DTC'S - diagnostic trouble code's stored in the (GEM)
Transfer Case -Electronic Shift on the Fly (ESOF) Operation The electronic shift on the fly (ESOF) system is an electronic shift 4x4 system that allows the operator to choose between two different 4x4 modes as well as 2-wheel drive. The operator can switch between 2WD and 4H mode at speeds up to 88 km/h (55 mph). To engage or disengage 4L range, the vehicle speed must be less than 5 km/h (3 mph), the brake pedal depressed, and the transmission must be in NEUTRAL.
The transfer case is equipped with an electromagnetic clutch which is located inside the case. This clutch is used to spin up the front driveline when shifting from 2WD to 4H mode at speed. When the control switch on the instrument panel is turned, the generic electronic module (GEM) recognizes that a shift has been requested and activates the electromagnetic clutch and the relays which power the transfer case shift motor. When the shift motor reaches the desired position, as determined by the contact plate position inputs to the GEM, power to the shift relays and motors will be removed. When the transfer case front and rear output shafts are synchronized, the spring loaded lockup collar mechanically engages the mainshaft hub to the drive sprocket. Finally, the front axle collar is engaged and the electromagnetic clutch is deactivated.
Shifts between 2WD and 4H can be made at any speed up to 88 km/h (55 mph). Listed below are the inputs and outputs needed by the GEM to execute a change between any of these modes.
Feature Inputs:

• 4WD mode switch (various resistances; go to Table 1).
• Contact plate position inputs A, B, C, D (grounded when closed, open circuit when open; go to Table 4).

Feature Outputs:

• 4x4 shift motor relay outputs (go to Table 2).
• Transfer case clutch relay (grounded when relay is activated, open circuit when relay is deactivated).
• 4x2/4x4 vacuum solenoid (grounded when activated, open circuit when deactivated).
• Cluster indicators (ground when activated, open circuit when deactivated).

When shifting into or out of 4L, the GEM requires that the vehicle speed be less than 5 km/h (3 mph), the brake is applied, and the transmission is in NEUTRAL.

Feature Inputs:

• 4WD Mode Switch (various resistances; go to Table 1).
• Contact Plate Position Inputs A, B, C, D (grounded when closed, open circuit when open; go to Table 4).
• Output Speed Shaft (OSS) Sensor (Sinusoid Signal: 0.7V-20V, 2.2 Hz/mph).
• Brake Input (battery voltage when brake is depressed, open circuit when not activated).
• Transmission Range Sensor (grounded when transmission is in NEUTRAL, open circuit otherwise).
• Start/Clutch Depressed Input (go to Table 3).

Feature Outputs:

• 4x4 Shift Motor Relay Outputs (go to Table 2).
• 4x2/4x4 Vacuum Solenoid (grounded when activated, open circuit when deactivated).
• Cluster Indicators (grounded when activated, open circuit when deactivated).
• P1804 Transmission 4-Wheel Drive High Indicator Circuit Failure GEM REFER to Section 413-01A . P1806 Transmission 4-Wheel Drive High Indicator Short Circuit to Battery GEM REFER to Section 413-01A . P1812 Transmission 4-Wheel Drive Mode Select Circuit Failure GEM REFER to the Symptom Chart. P1815 Transmission 4-Wheel Drive Mode Select Short Circuit to Ground GEM REFER to the Symptom Chart. P1820 Transmission Transfer Case Clockwise Shift Relay Coil Circuit Failure GEM GO to Pinpoint Test A . P1822 Transmission Transfer Case Clockwise Shift Relay Coil Short Circuit to Battery GEM GO to Pinpoint Test A . P1824 Transmission 4-Wheel Drive Clutch Relay Circuit Failure GEM GO to Pinpoint Test E . P1826 Transmission 4-Wheel Drive Low Clutch Relay Short Circuit to Battery GEM GO to Pinpoint Test E . P1828 Transmission Transfer Case Counter Clockwise Shift Relay Coil Circuit Failure GEM GO to Pinpoint Test A . P1830 Transmission Transfer Case Counter Clockwise Shift Relay Coil Short Circuit to Battery GEM GO to Pinpoint Test A . P1832 Transmission Transfer Case Differential Lock-Up Solenoid Circuit Failure GEM GO to Pinpoint Test C . P1834 Transmission Transfer Case Differential Lock-Up Solenoid Short Circuit to Battery GEM GO to Pinpoint Test C . P1838 Transmission Transfer Case Shift Motor Circuit Failure GEM REFER to the Symptom Chart. P1846 Transmission Transfer Case Contact Plate 'A' Circuit Failure GEM REFER to the Symptom Chart. P1850 Transmission Transfer Case Contact Plate 'B' Circuit Failure GEM REFER to the Symptom Chart. P1854 Transmission Transfer Case Contact Plate 'C' Circuit Failure GEM REFER to the Symptom Chart. P1858 Transmission Transfer Case Contact Plate 'D' Circuit Failure GEM REFER to the Symptom Chart. P1866 Transmission Transfer Case System Concern - Servicing Required GEM REFER to the Symptom Chart. P1867 Transmission Transfer Case Contact Plate General Circuit Failure GEM REFER to the Symptom Chart. P1876 Transmission Transfer Case 2-Wheel Drive Solenoid Circuit Failure GEM GO to Pinpoint Test C . P1877 Transmission Transfer Case 2-Wheel Drive Solenoid Circuit Short to Battery GEM GO to Pinpoint Test C . P1891 Transmission Transfer Case Contact Plate Ground Return Open Circuit GEM REFER to the Symptom Chart. Your best bet , take it to a qualified repair shop. Tapping on thing's isn't the way to diagnose

1. • 1 Start your Dodge truck's engine.
     
   • 2 Turn the electronic transfer case from "2WD" to "4WD Lock" to engage the high range 4WD, if the dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" to "4H." The electronic transfer case is located on the instrument panel and is marked with "2WD," "4WD Lock" and 4WD Low." The lever-equipped transfer case is located to the right of your leg and is marked with "2H," "4H" and "4L."
     
   • 3 Shift the transmission into "Neutral" while the vehicle is either stopped or rolling at 2 to 3 mph to begin engaging in the low range 4WD. Turn the electronic transfer case to "4WD Low," if the Dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" or "4H" to "4L."
     
   Tips & Warnings
   • Indicator lights will come on and alert you that your vehicle is in either the high or low range of 4WD.
     
   • Do not engage in the low range of 4WD drive if the transmission is in gear; you must shift to "Neutral" first.
     
   • Many Dodge trucks allow you to shift from 2-wheel drive to the high range of 4WD at up to 55 mph--consult your truck's manual to ensure that this is possible. Do not exceed 55 mph while engaged in the high range of 4WD. Do not exceed 25 mph while engaged in the low range of 4WD.
     
   • Do not engage in 4WD unless you are on slipper or rocky roads.
     

Lift and support the front of the truck so the front wheels are off the ground ( take safety precautions, chock wheels, jack stands, etc )
Key on, engage 4x4 and try to turn the front drive shaft.
If it turns it is a problem with the transfer case.
If it doesn't it is a front axle engagement problem.

I am going to guess the drive shaft will not turn, and the problem is the shift disconnect motor on the front axle, or the shift solenoids.
The shift motor looks like this


The shift solenoids look like this :


You can check the shift solenoids with a vacuum gauge. The blue vacuum line is the 4WD operation, the pink is the 2WD operation. Pull the vacuum line at the shift disconnect motor, and install the vacuum gauge. Shift into 4WD and the vacuum should be on the line, and hold. If not could be the disconnect motor or the vacuum line to the motor.

Could also be the shift motor in the transfer case, but with the 4x4 light on the cluster lighting up, the transfer case should have shifted, the confirm comes from the transfer case to illuminate the 4x4 indicator on the cluster.

2001 Mitsubishi MONTERO 01 - Transfer Case > POWER TRAIN : TRANSFER CASE (4-WHEEL DRIVE) [Part 104000 ]
TSB No: 0223007 NHTSA ID: , November 01, 2002 : Replacement:
Summary: 4wd indicator lamp flashing / diagnostic trouble code (dtc) 33.

2001-02 Montero
A flashing 4WD indicator lamp and/or DTC 33 may be caused by corroded transfer case shift position switches. The original switches are susceptible to water damage, and new revised switches are available to prevent the problem.

PROCEDURE

1. Replace the five transfer switches

2. Clear the DTC, using the scan tool.

3. Test drive the vehicle to confirm the 4WD indicator lamp does not flash and DTC 33 does not reset.