The BCM controls the interior illumination of the circuits controlled by the dimmer switch. These include the lamps in the cluster, door switches, radio, center console, etc.
The dimmer switch is an input to the BCM. it does not directly control the lights. The dimmer switch is controlling a GROUND path to the BCM, meaning it is a variable resistor to Ground that the BCM is reading to interpret the wished lamp setting of the driver. If you ground out pin 8 on the headlamp switch, or pin 20 on connector C2 on the BCM the instrument lights should come on full. (Wire color is Black with a White tracer, connector color is White)
The BCM wire that feeds all the dimmable lights is on pin 16, connector C2, color is plain Orange. This wire feeds + Power to all the lights. If you jumpered this wire to + voltage, all the lights should illuminate full. One burnt bulb will not prevent the others from working.
With a DRB-3 or other Scan Tool that will read the BCM system, you can read the inputs, and actuate the outputs of the BCM and read fault codes, which greatly simplifies diagnosis of the BCM controlled systems. The fault code for the Illumination control issue would be "PWM test Failed". If you have this code present, check resistance to ground on the pin 16, connector C2 Orange wire circuit, if over 5 Ohms, replace the BCM, if it is under 5 ohms, check the wiring for a short to ground.
Checking continuity, circuit resistances and connectors for corrosion may help determine if the Dimmer, BCM or the dash wiring is at fault.
Hope this helps!