It is cam shaft, but not for valves, it is for rocker arms adjustment. You right. The sensor tells to VVT angle of this shaft.
There is a way, how to test it. If you unplug the connector from the sensor, the car will run from buterfly valve only. VVT will be automaticaly set to fully open and stay there. The car should be operating normaly, but it will loose few hp.
Any news about the starting problem?