Well it's basically just a switch. So detach or unplug it and use a continuity meter on the two wires. In darkness there will be no continuity but there should be in good daylight.
The control box is designed to allow the boiler to light up, but if a flame is not established within about 20 secs it goes to lockout. It's the flame that provides the light to keep the photo cell switch closed.
Of course the control box itself may be at fault.
I had a old and faulty 'petercam' one, which I examined and found a small heating element which took it 20 secs to break the power circuit, unless of course power was provided via the photo cell, which I think operated a relay and cut the power to the heating element.
However with a new control box, I bench tested it first.
Wired in a bulb and bulb holder to represent the transformer and electrodes. Another bulb and bulb holder to represent the motor/pump assembley. And yet another to represent the solinoid.
Wired in the photo cell and put the cell inside a blanked off tube to keep it dark.
The bulbs operated exactly as they should. Went to lockout if I didn't remove the photo cell. or if I did then replace it or cover it.
I've have been further and run my boiler without a control box.
Supplied 3 separate 'switched'power supplies to operate transformer motor/pump and solinoid.
ie transformer ON, followed by motor/pump ON, followed by soliniod ON, boiler lights then, followed by transformer OFF.
Kept boiler running for about 10 minutes (no thermostat) then fitted control box.