Did you check that you are indeed having power to the system while cranking, not just with ignition on?
Yes, and the lamp seems to go out when cranking the engine over, suggesting a cut in the power (on the middle pin of the coil pack) The same also happens with pins 1 and 2 of the coil pack plug (the earths) As soon as the key is turned to engage the starter the test lamp goes out until the key is released
Check the resistance of the CPS sensor (in case the new one is duff) 200-400 ohms.
I havent got access to a resistance meter but have another known good CPS I can try
When you say it flicks, do you mean that it moves for an instant
No, it pulses properly as the engine cranks over