I have a 2001 ford mustang v-6 that the dome light will not go out when the doors are closed and the key is out ?

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 .

First, try turning the switch on the dome light to a position until the dome light goes off when the door is closed. Beyond that, you've got an electrical problem. . .

You need new door switches

sounds like your dome light switch is bad. it is in the door jam. thet wear out ,and act like the door is open when it is closed

• So your dome light is what you are referring too? Make sure your dim control is turned so the dome light is not set to on. There is a switch on the door that when the door is opened and closed the dome light goes on and off. Remove it and clean the contacts and try to see if that helps. If not you may need to replace the switch?

that sucks!
Its probably a wiring problem.
If: You close the door, the light stays on, and the car says "Door Ajar / Open" (Idk if you have a screen on the dash) or shows the door open symbol / light, then its a problem with the switch.
If it doesn't say its open, then it is a wiring problem elsewhere.. I would pull the fuse, and get it checked out. I dont know what your conditions are with the ford warrantee, but if you have one, i would bring it in for warrantee repair!
Good Luck!

The switch is built into the latch mechanism, you have to remove the door panel and reach inside the door to access it. You are on the right track, the switch is either sticky or loose.

I believe when you go to full brightness the dome light also turns on. If so check the dome light and door switches.

It should stay on for about 30 seconds and go off. Otherwise, the car is 11 years old, so find a switch position which does not drain the battery.

Not 100 % sure on the Mustang, but on F150 this is 1 of 2 places.

First check is if the dome light comes on. If not, check the door switch, and the wiring between the door and the A pillar for a broken wire ( F150 this is a Black w/ yellow wire ).

Second, in the driver's side door sill, under the trim plate, there is a splice in there, that is only in tape. The F150s ( 04-08 ) can have water in the sill with the splice, and it freezes and stops working.
A lot of wires to look through, but you find something similar.
The door sill usually has other issues with it, apart from the radio saying on.

Start with looking through the door to A pillar harness, if your adio stays on, and you don't have dome lamps