I have not seen that many headlight switches in my life but I think I can say with some degree of confidence that this is certainly not normal. You mentioned that the ignition switch appears to have been replaced some time before you bought the truck. The following is from the system description for the "Passlock Theft Deterrent;
Passlock is a vehicle theft deterrent system. This system contains a Passlock sensor. The Passlock sensor is part of the ignition lock cylinder assembly. The BCM provides power and ground for the Passlock sensor.
When turning the ignition switch to the start position with the proper key, the Passlock sensor generates an analog voltage signal. This signal is sent through the Passlock detecting circuit. This analog voltage signal is of a specific value to the vehicle, and varies from vehicle to vehicle. When attempting to start the engine, the BCM compares a preset stored analog voltage value with the signal coming from the sensor. Because both values match, the BCM sends a fuel enable password via the Class 2 serial data link to the Powertrain Control Module (PCM) /vehicle control module (VCM) . As a result, the PCM/VCM allows fuel delivery to the engine.
When attempting to start the engine by means other than using the proper key in the ignition switch, the Passlock sensor sends an analog voltage signal of a different value. The BCM compares the preset stored analog voltage value with the signal coming from the sensor. Because both values do not match, the BCM sends a fuel disable password via the Class 2 serial data link to the PCM/VCM. As a result, the PCM/VCM disables the fuel delivery to the engine.
According to the GM replacement procedure there are two separate re-learn procedures that may have to be performed after replacement of the ignition switch. PASSLOCK Reprogramming Auto Learn and Seed and Key (Scan Tool) Learn. Don't know if these were performed or if they would fix the problem with your security light. If the jumper is installed the way you state then the ash tray light and the backlighting on the switches on your doors (windows, door locks, outside mirrors) would always be lit and the battery would drain. It is not at all clear from the drawings how removing that jumper would prevent the truck from starting. I can only guess that somewhere on the truck there is additional jumper(s) or lifted or cut wires that is causing (allowing) this truck to work the way it is. It would be interesting to see what the wiring at the BCM looks like. I think if it was me I wouldn't kick a sleeping dog. As long as it has not burned the truck to the ground and you are happy with it keep driving it. Maybe CarMech97 is correct and this is a redneck security system.
I am sure there is a better man than me on this forum than can figure this out given enough information and time.