I wanted to disable mine too, I yanked the TJ's out so I figured why bother having it. Well, the JK uses it for all sorts of warnings, so I decided to keep it, but make it quieter. I also didn't want to risk screwing up a bunch of stuff due to the CANBUS crud the JK has either.
So, here's the fix (based on a 2013). First remove your dash cover on the driver's side. Start by pulling the panel off under the steering wheel, just pull it from the top using your fingers, it's clipped in (be careful with the clips).
Then unscrew the two screws on either side of the steering wheel. The piece includes the area around the stereo too. Using the area by the steering wheel, reach behind it and pull firm and slow to get the panel released. It has a bunch of the same plastic tabs as the first piece.
Now you'll see the instrument panel. Unscrew the screws there, unclip the harness from the back by pushing in the tab, and remove it. Put the instrument panel face down on a soft towel (plastic front scratches easy). Use a small flat head screwdriver to pry the clips open all the way around the back of the unit. (See below in orange.) You'll see a circuit board when you open it.
On the upper right side of the circuit board there's a round buzzer (see below in green). In the TJ's the solution was to grab onto it firmly and twist it off, leaving two soldering wires broken off at the board. It was here I debated whether I might screw up the CANBUS and decided to mod it instead. The small hole in the middle of the buzzer allows the buzzer to 'breathe' and blocking it reduces the amount of noise produced - however - it also can make it sound buzzy instead of beepy. I found that instead of blocking it off with tape (works but buzzy), it works better to use a piece of 1/4 sponge over it. Doing this will quiet the beep but not create a buzzy annoyance. You can adjust the sponge as needed, or tape over it with duct tape and a sponge and it will go away. The bad part of adjusting it is you have to plug it back in to test it - the harness tabs made my fingertips hurt after a few tries.
Put it back together again and done.