Dome light

Looks to be a pretty simple system. When in the door position, if you open either door, it does not turn on the light? If this is the case, then I doubt both door switches have gone bad at the same time. If it only happens with one door or the other, suspect the door switch that doesnt work. If it doesnt work with both doors, then I would suspect the light itself may be bad.
If you have access to a volt ohm meter, then you can remove the doem light and trouble shoot from the plug on the light. You should have power to pin 2 of the plug since the dome works in the on postion. You can check for a ground on pin 1 when your door is open. If you have a ground, then the light itself is bad. If you dont, I would suspect the integration relay. I doubt both door swtiches have gone bad at the same time.
Good luck