2002 TrailBlazer Powerup Sequence as seen at the Instrument Cluster.

Here I show the sequence of events at a 2002 TrailBlazer instrument cluster during a normal startup.
The turning of the iginition switch/key is slowed to allow better observation of the various displays.
The first stop is actually between OFF and ACC where ignition switch terminals F (red wire) and E (white wire) close sending both "Ign D voltage" (rear fuse #50,3A) and "Accessory voltage" (rear fuse #31,3A) to the BCM at terminals C3,A18 and C3,B15 respectively, as well as " Ign 0 Input" to the PCM at terminal C1,21. Also energized at this point are the transmission shift solenoids and terminal F of the shift lever/ignition lock switch. At this point is where the battery lamp and the transmission range display illuminate. There is no change to the circuit powering of the cluster at this point. Everything that changes on the display is solely the result of BCM, PCM, and cluster communications. Look for the presence of the indicator bar under the PRND321 display which confirms PCM to Cluster communications. Based on experimentation I believe the battery lamp illuminates in response to a "Network Control" status announcement from the BCM. The battery lamp will remain on until after the bulb check in the RUN position.
The second stop in the video is at the ACCessory position. Here ignition switch terminal B (red/white wire) connects to terminal A, the brown wire. This sends "TBC ACC" signal power through fuse #31,3A to the BCM at terminal C3,B15. The BCM sends another different "Network Control" message out. In the video it is dark out so the background illumination comes on. Also powered in ACC are the front windshield wipers and the rain fuse which, depending on options, powers the DVD player and moisture sensor for the wipers.
In bench tests of an ignition switch I could isolate two separate connections that occur next but in practice cannot so I will present them as one station, the RUN position.
Turning the key to RUN connects the aforementioned Ignition switch terminal F (red) to terminal G (orange) while maintaining the previous connection to terminal E (white). Also connected at this key location is ignition switch terminal B (red/white) to terminal C (pink), again maintaining the previous connection to terminal A (BRN). The BCM again announces the vehicle status with a different "Network Control" message. There are simply too many circuits brought online by these two connections to callout here in detail so I will name the major systems.
Terminal G (orange) brings up the HVAC system, the 4WD, and one more connection to the BCM: the "IGN B Voltage" input (rear fuse "TBC RUN" #52,3A) at C3:A20.
#Terminal C (pink) powers up the 6 fuel injectors, the 6 ignition coils, the engine cooling fan relay (45, through underhood fuse #20,10A), the O2 sensor heaters, the EVAP system purge and vent solenoids, the SIR system, various terminals of the park/neutral and brake switches, and so on. More significantly for this video it connects "Ign 1 Voltage" to the BCM at C3:A19 via rear fuse #16,10A, "Ignition 1 Voltage" to the instrument cluster at terminal B7 via the underhood "Ign E" fuse #22,10A, and "Ignition 1 Voltage" to the PCM at C1:19 via underhood "PCM 1" fuse #28,15A.
Upon entering the RUN state of key position the cluster will perform a bulb check illuminating all indicator lamps. I believe some of these lamps are lit up for a specific time period and some depend on other modules to command them off. I know the security lamp is turned off by command messages from the BCM for example. The gauges will move to the locations commanded by the module responsible for the particular gauge. The PCM commands the Oil Pressure, Fuel Level, and Engine Temperature gauges through the serial data bus. The PCM also controls the Tachometer and Speedometer as well as the "Service Engine Soon" lamp but does so through direct wiring to the cluster as opposed to serial data. The BCM commands the DC Voltage gauge.
At completion of the transisition to the RUN position, but before turning the key any further the "Service Engine Soon" lamp should be on, as well as the PRND321 display and the DIC/odometer and also the gauges should be at their proper locations. If dark out the background lighting should be on.
Turning the key to the START position DIS-connects ignition switch terminals G (orange) and A (brown) from 12 volt power. The BCM sends out another "Network Control" message announcing the current status of the vehicle. The DIC/odometer and PRND321 turn off. The "Service Engine Soon" and background lighting remains ON during starter engagement. At engine start the "Service Engine Soon" light goes OFF and the cluster performs a reset, sweeping gauges to zero and performing another bulb check, a difference being the "Service Engine Soon" light remains OFF. As the key returns to the RUN position terminal G (orange) and C (pink) are reconnected to 12 volts. All gauges resume normal operations.

[@themetalmike187]

Your seatbelt light doesn't come on either. Did you do that or is it a common issue?