Door ajar light & chime go off while driving.

There is no fuse just for door ajar chime.

Door Ajar Warning Chime The door ajar warning chime warns that a door is ajar. The door ajar warning chime is a single chime with a 1 second duration. The door ajar chime sounds when the driver or passenger door becomes ajar while the ignition switch is in the ON position.
The door ajar warning chime inputs are:

• the ignition switch ON position
• the door ajar switches

The output is the instrument cluster chime.

Something is not telling the car your door is closed check the light switch make sure it's pushing In and properly and getting contact

the door jam switch is located on the door latch very hard to see but may be visible with a compact mirror it is a single wire unit sorta round about 1 inch long

did you RTM read the operators guide yet,
it tells you why all beeps beep and what lamps flash, (warning) and why. did you?
you turn on, the head lights, (what about 1st click , parking lights"?)
and does the dash cluster, show warnings of any kind?

if a door is ajar the system will think, you are exiting veh. with lights on and tell you, buy beeping ,etc.
but on my jeep it says on the dash DOOR, or on EVICs, (not yours)
the newer car even tells what door IS AJAR.
mine on shows , "DOOR"
the operator guide will say, check all doors for ajar, and get warning clear before driving....etc.

if you lost the guide here it is for free

http://justgivemethedamnmanual.com/jeep/jeep-wrangler-owners-manuals/

click the 05 link
ignore beeps, there are just too many .. i look at the cluster and learn to read it..
my newer jeep 08 can produce 1000s of errors,,,,, possible.
in fact the intent it to beep to tell the driver to look at the cluster
for in depth, causes.
see chapter starting on page 136'

once sound it makes is Check gauges chime. so check them.
and headlamps left on
and door ajar.

page 63
NOTE: If the driver's door is left open, and the headlights
or parking lights are left on, the "High Beam
Indicator Light" will flash and a chime will sound.
Lights-On Reminder
If the headlights or parking lights are on after the ignition
is turned off, a chime will sound when the driver's door

its a crude system, and evolved to complex in 2007.
"DOOR" or RF-door , on mine.
or

NOTE: A tone will chime if the turn signals are left on
for more than 1 mile (2 km).

search manual for
"chime will sound"

look for a swich in the door fram itself .replace it and make sur its getting good contact to door jam

Could be the sensor in the key switch telling you the key is still in the lock.

this problem is caused by a tiny micro switch that is attached to the door latch inside the doors, the stick and give this false warning, have replaced dozens of them, it is called the "door ajar" switch oddly enough :)

door jamb switches are bad unplug one at a time till you find it dont forget tailgate

Probably a faulty door switch. Are you familiar with what I'm talking about. Little push like switches that the doors push on as they close, usually on door post by latch end, or sometimes in jamb of door at hinge end.

HI.
ON Ford cars and Suv's,
Some times the sound chime after the seat belt buklet.
Is like a open door.
The problem on this car is that the the DOOR AJAR SWITCH. come danaged. and the Body cumputer don't recievethe door close signal.
But is intermitent.
The door ajar switch is on the door lacth.
You only can get front the dealer.
OK. I hope this information can be useful for you.

Thank you.