Where is the BCM located on a 2002 Chevy Trailblazer

Should be located under the shift console or right in that vicinity. Hope this helps you in locating your BCM, Jesus loves you, John 3:16-17 (KJV)

The BCM is attached to the fuse block under the second row seat on the drivers side.

Is the SERVICE 4WD indicator lit ?
The SERVICE 4WD indicator is an integral part of the cluster and cannot be serviced separately. This lamp is used to inform the driver of the vehicle that a transfer case system malfunction. The SERVICE 4WD indicator is controlled by the transfer case shift control module via Class 2.
If so suggest you take it to a ASE certified repair shop !

Most times it is the light switch when none of the lights work. Can you manually turn them on? This over rides the BCM. Interior lights are controlled by the BCM. Try opening the passenger side door, see if they come on. If so, replace the drivers door latch, inside the door. If still no lights. The BCM needs scanned for codes.

Does yours have The Selectable Four Wheel Drive (S4WD) Front Axle or
Automatic Four Wheel Drive (A4WD) Front Axle is
The SERVICE 4WD indicator lit ? do you have any other lights lit ?
anything like this happen Transfer Case Shift Control Switch Indicator Flashes, then Returns to Previous Mode ? Your going to need to take it to a repair shop , have scan tool hooked up an check for codes in the BCM an all the modules !

First thing is to check the fuse. If the fuse is ok,then the shift fork motor might be bad

There is no separate fuse for the courtesy lights, the BCM (Body Control Module) has two fuses associated with it. They are located in the rear fuse panel, and are fuse #4 and 40.

There is no fuse marked for dome light's in the rear fuse box. The BCM - body control module controls the dome / courtesy light's .
The body control module (BCM) monitors the courtesy lamp switch signal circuit in order to determine when the courtesy/dome lamps should be illuminated. When the BCM senses that the courtesy lamp switch signal circuit is grounded when the switch is activated, the BCM will directly illuminate the courtesy/dome lamps.
DTC B3801 Passenger Compartment Lamp Request Circuit

You should possibly think about taking your vehicle to a qualified repair shop !
Install a scan tool.
Turn ON the ignition, with the engine OFF.
With a scan tool, observe the courtesy lamp switch parameter in the body control module (BCM) data list.
Does the scan tool display INACTIVE?
YES - Go to Step 3
NO - Go to Step 4
3
Activate the courtesy lamp switch.
With the scan tool, observe the courtesy lamp switch data parameter.
Does the courtesy lamp switch data parameter change state?

• Test the courtesy lamp switch for sticking in the ON position.
• Perform a visual inspection for loose or poor connections at all related components. Refer to Testing for Intermittent Conditions and Poor Connections in Wiring Systems.

https://sparkys-answers.com/2010/11/2003-chevrolet-trailblazer-blower-not.html

I have a 2002 chevy trailblazer 4x4 control light not working. when trying to switch from 2wd to 4wd nothing happens. no ligth no engaging of the drive