May not be helpful but since it's CDS it should be a simple circuit. (HA! that's what they all say).
If you're just messing with 'em start with the battery compartment and switch. Look for corrosion and/or broken wire,
maybe a bad wire. If this has the CDS on a swing out arm the wires where it flexes would be suspect. CDS cells themselves
have a high mortality rate, The cell itself can be tested with a volt/ohm meter, it should change resistance when exposed to light.
Don't remember if it needs a voltage applied or not.