Interior dome light stays on when driving.

Interior lights and the power door locks are controlled by a electronic control module . Hooking up a factory or some other type professional scan tool an checking for codes an viewing input data to these control modules would be the first thing to do.
The interior lighting system consists of the following:

• lighting control module (LCM)
• driver door module (DDM)
• instrument panel
• dome/map combination
• courtesy/reading lamps
• orientation light
• door lamps
• footwell lamps
• luggage compartment lamp
• glove compartment lamp
• vanity mirrors
• door ajar switches
• viewing wiring diagrams an checking power and ground circuits for these modules would be the next step if no codes were found . Principles of Operation
  Lighting Control Module This vehicle uses a lighting control module (LCM). The LCM is a microprocessor-based module that controls several vehicle subsystems, responds to electrical input signals from various switches, sensors, and external modules and is located on the LH side of the instrument panel. LCM subsystem functions include:
  
  • headlamps with autolamps
  • turn signal lamps/hazard flasher lamps
  • cornering lamps
  • parking lamps
  • daytime running lamps
  • interior lamps
  • demand lamps
  • battery saver
  The LCM interfaces with the driver door module (DDM) via the standard corporate protocol (SCP) network for the illuminated entry feature.
  The interior lamp is illuminated by pressing the individual interior lamp switch. The interior lamp is also illuminated by door ajar switches located in the door latches, when any door is opened. A theater lighting feature gradually increases or decreases the light intensity when switched by opening or closing a door.
  The dome/map lamp combination are located on each side of the interior lamp. The map lamps are operated independently of the interior lamp by two switches located on the interior lamps.
  The interior lamps are illuminated by holding the panel dim switch in the UP position until the dome lamps turn on. The interior lamp also illuminates when a door is opened and actuates the door ajar warning lamp switch in the door latch.
  The front map lamps are powered by the demand lighting circuit and the interior lighting circuit.
  The rear passenger reading lamps are incorporated into the rear seat assist handle and are located over the rear door openings. These lamps are illuminated through power supplied by the LCM demand lighting circuit.
  Interior lamps (controlled by the LCM) are activated by using the dome lamp switch (instant ON/OFF response) or when a door is ajar. The following lamps illuminate for interior lighting:
  
  • instrument panel interior lamps
  • front map lamps
  • rear reading lamps
  • door lamps
  Demand lighting includes lamps that are illuminated by the customer by directly actuating a switch. The front dome/map lamps are located in the overhead console. Each lamp is controlled by its own switch.
  The following demand lamps are powered by the demand lighting output of the LCM:
  
  • glove compartment lamp
  • vanity mirror lamp
  • luggage compartment lamp
  Each lamp has a dedicated switch that closes to ground to illuminate the lamp.
  The front map lamps are powered by either the demand lighting circuit or the interior lighting circuit, depending upon the position of the switch associated with each lamp. When the customer turns the front map lamp switch ON, the front map lamp is illuminated through power supplied by the LCM demand lighting circuit. If the customer moves the map lamp switch to the OFF position, the power from the LCM demand lighting circuit is interrupted and the lamp is reconnected to the interior lighting circuit.
  The rear reading lamps are powered by either the interior lighting circuit or the demand lighting circuit.
  The luggage compartment lamp is controlled by the trunk ajar switch, and is powered by the demand lighting output from the LCM, and is mounted near the center of the upper rear panel.
  The glove compartment lamp system consists of a glove compartment lamp switch and wire and miniature bulb assembly. Opening the glove compartment door closes the switch which provides power to the glove compartment lamp switch and wire. The glove compartment lamp switch is grounded to the body sheet metal.
  The vanity mirror lamp system consists of a switch and bulb assembly in the RH inside visor and the LH inside visor. Lifting the vanity mirror cover closes the vanity mirror lamp switch and provides power to the lamps.
  The illuminated entry system is controlled by the LCM and provides interior lighting upon entry to the vehicle.
  Interior lamps will be illuminated for 25 (±1) seconds which includes a theater lighting ramp-up time (0.5 seconds). This time interval does not include the theater lighting ramp-down time. Interior lamps will be turned off before the 25 (±1)-second timeout if the ignition switch is turned to the RUN or ACC position.
  The illuminated entry system has the following additions to accommodate the remote entry system: pressing the unlock button on the remote transmitter will activate the illuminated entry system (with theater ramp-up). When the driver door module detects a button press, it sends a signal on the J1850 communication network activating the interior lamps. The lighting control module will turn off the lamps by sensing the all doors lock signal.
  The battery saver feature prevents excessive drain from loads inadvertently left on. When the ignition switch is turned OFF, power is interrupted to the interior lamps and headlamps (after a 10-minute timeout) and the demand lamps (after a 30-minute timeout).
  The battery saver has the following inputs:
  
  • luggage compartment door ajar switch
  • dome lamp switch
  • ignition switch status
  • illuminated entry signal
  • headlamp switch
  • driver/passenger door ajar entry switch
  • keyless entry remote transmitter
  • door unlock, luggage compartment door release

The door switch doesn't go to the dome lights , the switch (door ajar switch ) is an input to the SMJ - smart junction box or body control module take your pick .
Principles of Operation
When the SJB detects a request for lighting, it turns on the interior lamps by supplying power to the lamps. The request for lighting can be an open door signal from a door ajar switch, an interior lighting on command from the instrument panel dimmer switch or an unlock command from a remote keyless entry (RKE) transmitter.
The door ajar switches are hard-wired directly to the SJB. The 2 door ajar switches are normally closed when the doors are closed. The decklid ajar switch is normally closed when the decklid is closed. All door ajar switches receive voltage from the SJB and each has its own ground circuit.
The instrument panel dimmer switch receives a ground signal from the SJB. The instrument panel dimmer switch provides variable resistance for backlighting the instrument cluster and a toggle ON/OFF function for the interior lights.
The RKE receiver is contained inside the SJB. When the SJB receives an unlock request from an RKE transmitter, it unlocks the doors and turns on the interior lamps. There could be DTC'S diagnostic trouble codes stored in the SJB ! You can not access these codes with a OBD2 code reader , need a factory scan tool .
B1319 Driver Door Ajar Circuit Failure Go To Pinpoint Test D . B1327 Passenger Door Ajar Circuit Failure Go To Pinpoint Test D . B2021 Dome Lamp Input Return Circuit Failure Go To Pinpoint Test A . B2550 Dome Lamp Output Circuit Short to Ground Go To Pinpoint Test A . B2554 Dome Lamp Output Circuit Failure Go To Pinpoint Test D . Do you know B-codes -body control .
Your best bet is to take to a ASE certified repair facility or a Ford dealer .

its either a bad door switch,or could be the dome override switch by headlight switch,or your interior light switch is all the way up

your control module is faulty..

one or more of the door switches are malfunctioning

The interior lamps system consists of 2 main features. Illuminated entry and a battery saver feature that will turn the interior lights off after 20 minutes if they are left On with all doors closed and the ignition Off. The body control module (BCM) controls both of these functions. Battery power is supplied by the BCM through CKT 1732 to the following lamps:
• The dome lamp
• The map lamps
• The rear reading lamps
• The rear dome lamp
• The cargo lamp
• The glove compartment lamp
• The courtesy lamps
• The sunshade lamps
The BCM also controls the ground circuit side of the dome lamp and reading lamps for illuminated entry. The dome lamp and reading lamp will remain on for 20 seconds after the ignition key is removed and the last door is closed. In addition, if the vehicle is equipped with remote keyless entry (RKE), the dome and reading lamps will turn On and stay on for 20 seconds after an UNLOCK signal is received from the keyless entry transmitter.
The reading lamps, dome lamp and map lamps can be turned On at any time by moving the appropriate switch to the On position.
The rear dome lamp is fed battery voltage through CKT 1732 from the BCM, through the liftgate ajar switch, and is grounded through CKT 650 to the rear ground splice pack. The rear dome lamp will turn on when the liftgate is opened. The cargo lamp is fed battery voltage through CKT 1732 from the BCM, through CKT 744 and grounded through the decklid ajar switch.
The courtesy lamps are fed battery power through CKT 1732 and are grounded through CKT 745-- left front, CKT 747--left rear, CKT 748--right rear, CKT 746--right front. These circuits will ground through the door jamb switches. The courtesy lamp will be illuminated when the affected door is opened. For example, when the right rear door is opened, the right rear door courtesy lamp will turn on.

Not a fuse problem , if the BCM had blown fuse other thing's wouldn't be working as well . . Probably wiring or BCM . Using factory diagnostic,s instead of guessing as to what the problem is , is the proper way .

Interior Lamps Diagnosis
Symptom
Procedure
Important: Before proceeding with these diagnostics, check for DTCs. If DTCs are present, complete the associated diagnostics. If the condition still exists, return to this chart.
All of the interior lamps are inoperative when any door is opened.
Chart 1
The dome lamp is inoperative in the ON position, but OK in the door position. The map lamps operate normally.
The dome lamp switch is faulty. Replace the dome lamp switch.
The dome lamp is inoperative in the DOOR position, but is OK in the ON position.
Chart 2
The dome lamp is inoperative in any position and both reading lamps are inoperative.
Disconnect the dome lamp connector (BLK 3-way).
Check for voltage at terminal "C" CKT 1732 ORN wire.
If OK, the dome/map lamp is faulty. If no voltage is present, there is an OPEN in CKT 1732.
Either the right or the left sunshade mirror lamp is inoperative.
Chart 3
Either the right or the left rear reading lamp is inoperative in the ON or the DOOR position.
Chart 4
The rear reading lamp is inoperative in the ON or the DOOR position.
Chart 5
Battery rundown protection is shorted to ground - B1482.
B1482
The left rear reading lamp is inoperative in the ON or the DOOR position.
Chart 6