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Hello, on your 2013 F350 the lighting is controlled by the BCM (Body Control Module) The BCM is capable of monitoring all lamp circuits and can even shut down individual circuits if it senses a problem such as a shorted circuit. The BCM constantly monitors for electrical problems and if any are detected it may take action to prevent damage to the circuit as well as storing a DTC (Diagnostic Trouble Code) In some cases though the BCM can malfunction internally causing some lights to stay on or some to not work at all or both. It sounds like your BCM has an internal issue and may need to be replaced or reprogramed.
If you were adding a back up camera you could have created a positive or negative short if you spliced into the wrong wire. If you hvenot already done so unhook any wires you added and see if the problem persists. If imthe prblem still continues i would recomend taking it to a dealer. I know most people dont like taking their vehicles to the dealership but i think that would definetly be your best option. On average you can expect to pay around an hour for diagnosis and around an hour for reprograming. Most dealer rates range between 100-130 an hour. Modules can range from a couple hundred dollars to allmost a thousand.