Rear drivers side door ajar light flashes and beeps continually while driving

Sounds like one of the doors are not closing all the way!
If not closed completely there is not good contact at the switches making it seem like a door is partly open when breaking!
Check all doors for tight close and adjust or repair. Including rear hatch !
Also look at the information center on dash (if still lights up) it should say which "Door is Ajar" when the beeping\lights flashing is occurring.

Your best bet would be to find a Tech like this guy , with the right diagnostic equiment . Door Locks Go Crazy 1 Unless you know how to do automotive electrical testing . Your door ajar switch is a input to a body control module . or GEM as ford calls thiers .
Door Locks Go Crazy 2 Your auto lights are controlled pretty much the same .
Electric Testing Techniques You Need to Know

Do you know what DTC"S are ? diagnostic trouble codes ! You probably have a door ajar switch problem . You need a factory or professional type scan tool to check these codes
B1322 Door Ajar Driver Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1323 Door Ajar Lamp Circuit Failure GEM/CTM REFER to Section 413-01 . B1325 Door Ajar Lamp Circuit Short to Battery GEM/CTM REFER to Section 413-01 . B1330 Door Ajar RF Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1334 Decklid Ajar Rear Door Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1338 RR Door Ajar Circuit Short to Ground GEM/CTM REFER to Section 417-02 . B1340 Chime Input Request Circuit Short to Ground GEM/CTM GO to Pinpoint Test C .

• The Autolamps Are On Continuously

• Circuitry.
• Headlamp relay.
• Light sensor amplifier.

• Go To Pinpoint Test H .

• The Autolamp Time Delay Is Inoperative

• Fuse(s).
• Light sensor amplifier.
• Headlamp switch.
• Circuitry.

• VERIFY parking lamp operation. If OK, REPLACE the light sensor amplifier. If any parking lamp concerns exist, Parking, Rear and License Lamps REFER to Parking, Rear or License Lamps.

Do you see how complex these systems can be for someone that doesn't deal with these problems on a daily base's ! Check for codes an if there are any , doing the diagnostic's associated with it . Without doing the diagnostic's you could replace parts all day long an not fix the problem .
2002 2005 Ford Explorer Door Ajar Light Common Door Wiring Faults

Could be just a glitch. The BCM controls the beep through the radio. Thats why you hear for the speaker/drivers side. There are three possibilities for the beep. Door ajar with the key in the ignition, turn signal on too long, and seat belt unbuckled with the car running. Check for lights in the dash. no door ajar light, no seatbelt light. That could be the problem.

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"

clean and lub your door closing mech.

scotch brite the contacts , see if that helps.

My van did this aswell, you must have a power sliding door, when it is not latched properly this warning goes off but it won't say on your message center "door ajar". Stop and reopen the door and close it again no more bell. good luck.

door switch is not working.

take the small black cover off from the pillar side of the switch and use the straw with the wd-40 can and lubricate the switch well.. old ford tech trick

Try spraying WD-40 into the door latching mechanism (door side). I learned this fix after two battery replacements, but have only had to spray twice in the more than seven years of ownership