Something is definitely wrong, the fault should be logged as soon as the engine has been started, not once it has been run then switched off and on again. In this statement (Hall effect camshaft position sensors typically have three terminals; one for current feed, one for ground and one for the output signal)
Three wires, live, earth, signal. The specialist said "No live data is coming out of it?being received" If that were the case, there would be no spark and the engine wouldn't run.
On many engines with distributorless ignition systems and sequential fuel injection, a camshaft position sensor is used to keep the engine's control module informed about the position of the camshaft relative to the crankshaft. By monitoring cam position (which allows the control module to determine when the intake and exhaust valves are opening and closing), the control module can use the cam position sensor's input along with that from the crankshaft position sensor to determine which cylinder in the engine's firing sequence is approaching top dead center. This information is then used by the engine control module to synchronize the pulsing of sequential fuel injectors so they match the firing order of the engine. On some applications, input from the camshaft position sensor is also required for ignition timing.