You said something about the engine can run without the cam sensor.. That's not completely true. The engine needs a functioning cam sensor in order to start. If the cam sensor fails while the engine is running (this is the case for most failures), it will continue to run.. But once the engine is turned off, it will not restart.
If I remember correctly, the "common" or ground wire for all the engine sensors is the same color, sometimes with a trace. Look for that on the cam and crank sensors.. The other wire at the sensor carries the signal.. Remember, these two sensors generate the signal and send it back to the computer, not the other way around. In order to trace the wiring you really need an accurate wiring diagram.. It's common knowledge that some of the aftermarket service manuals contain inaccurate information. If possible, obtain a genuine GM service manual.
A "quick search" for "2003 Silverado Wiring Diagrams" turned up this site: You'll need to register to gain access...
https://portal-diagnostov.com/en/roo...ring-diagrams/