The petcock is vacuum operated. When the tap is set to ON or RES and the engine is running a vacuum is created by the carbs via pipes from the petcock which opens a diaphragm and lets the fuel flow. When the petcock is in PRI position this bypasses the need for the vacuum.
It is my thoughts the vacuum pipes have not been correctly installed. There appears to be 2 different ways of these being fitted. On the CSR model each carb is connected to 2 legs of a ‘T’ fitting. The 3rd leg is then connected to the petcock. The Y LTD model is connevted differently which Michael described in another thread recently. I will try to find a link. I am not sure which way the S LTD model should be but probably either would work.