If the door switch is bad or bulb is bad you'd still have 12V at the light. The light should always have 12V, the switches provide a ground circuit. So, make sure you check the red/green wire at the light with KNOWN good ground in the car.
If you have 12V, then its a grounding problem. If you don't, then the switches, etc don't matter, its a problem on the + side of the circuit.
I don't know what the green wire is in the pic, but is that a bare wire exposed? Definitely fix if so.