In Ford vehicles, the BCM (or GEM) is a computer component that monitors, regulates, and operates a slew of electronic components in your truck, such as the power windows, central locking, air conditioning, engine immobilizer, your dome light, and more. If the BCM malfunctions or is faulty, this can prevent the dome light (along with other vehicle functions) from working properly. According to RepairPal, the cost of replacing a BCM ranges from $560 to $600.
Another issue could be one of your truck’s doors. A misaligned door or a loose hinge can prevent a door from completely latching, meaning the circuit powering the dome light isn’t interrupted (i.e., turned off). So, even if your door looks closed, it might not be latched properly, thus causing that dome light to stay on.
Take your truck to your Ford dealership to get the issue properly diagnosed and fixed.