[EDIT/UPDATE:
NOPE. Just confirmed that cutting the chime-feed wire triggers a "NO BUS" message at the odometer and disables/scrambles cluster functions.
Suggestions to cure the door chime by jamming the sensor/plunger at the door itself WIN.
At some point I may try removing the chime itself from the cluster. If so, will report.
I'm going to leave the useless rambling below in case somehow it's useful to somebody. If nothing else as a warning NOT TO CUT CLUSTER WIRES!
___________________
[FOR ENTERTAINMENT ONLY: DO NOT CUT CLUSTER WIRES!]
On the instrument cluster plug, meter-confirmed that the VioletStripe/White wire is the DOOR chime feed. The seatbelt feed is a different wire, but they both activate the same insufferable chime.
After a 1/2hr failing to elegantly remove the wire's tab from the plug I cut/taped the wire; adios door chime:

HOWEVER, the chime still bleats a few times on key-insertion before muting. I have my turbo & manifold(etc) off so can't start the jeep to confirm 100% whether anything besides the door-circuit was affected. Given it will be a few weeks before my garrett arrives, if another member is aching to cut the wire to douse the door chime, test-drive & report back, great!
-I'll hack this post into digestible form shortly-]
I currently have multiple systems disassembled, including the dash. Great time to locate, remove and DESTROY the grating "Door Ajar!" chime. Sorry, but the pencil solution doesn't float my boat...
In another thread, someone referenced that it was suspected to reside within the instrument cluster. Yup.
Below is a step-by-step guide to access, remove and obliterate that rotten infuriating p.o.s. This is also a guide for replacing any burned-out instrument cluster bulbs.
And your tweeters!
I'll endeavor to improve the post by updating the instructions & pics.
Please offer corrections where I am mistaken.
REMOVAL PROCEDURE IN PICS (thx to WW for the steer towards "postimages.org"!):





More pics coming.
The chime is located directly above the tach at the top edge of the instrument cluster. It's black plastic cover looks like a donut-hole sized hockey puck:
A few advance considerations before preying upon the squawking rat-bastard chime:
- NOW will be the time to replace any burned-out instrument cluster bulbs! Take a pic of your entire instrument cluster immediately after turning-on the ignition; while it goes through the self-check sequence and all the cluster lights are briefly illuminated. Do a thorough evaluation whether any of your instrument cluster bulbs may have burned-out. If so, procure the correct bulb(s) in advance.
- You will also be removing the three pieces of trim which hide access to your audio's dash-mounted high-frequency drivers (tweeters!). You may want to evaluate the tweeters! condition/performance in advance to determine whether you need/want to replace/upgrade. If so, procure replacements in advance.
- While they're exposed and accessible, it's also an opportunity to do some cleaning of your vent-ducts and general inner-dash dusting. Procure/prepare your preferred cleaning products/tools.
Post-Op Notes:
While chilling chimelessly in serenity with your doors open, don't forget to rotate the dashlight dimmer hoop on the light-switch arm until the overhead lights go off (=Battery conservation).
[To be con't]
Keys: door open chime dash lights dead annoying ringing dinging clanging psychosis inducing antagonistic freaking bell weak piccolos no bus message No Bus NO BUS