Four days ago, my 2005 SRT-6 began to make a beeping/squealing sound coming from the dash on the passenger side.

The sound is high pitched.
It lasts anywhere from 1 to 5 seconds in length, with quiet periods of 0.5 to 20 seconds in between.
The sound only occurs while in motion.
It is coming from the interior, and cannot be heard from the exterior.
I've tried turning off the A/C, and that has no effect.
It occurs while accelerating, coasting, and breaking... if the car is in motion, it occurs.
It doesn't seem to be effected by speed -- it occurs equally in frequency at 5mph and 70mph.
It occurs both when the radio is on and when it's off (it's coming from the dash, not the speaker).
It occurs both in turns and while driving straight.
There are no lights indicating there is an issue (except the low tire pressure light is constantly on, but that's been on regardless of tire pressure for over a year. I've learned to ignore it).
The crossfire has 58,000 miles if that's relevant.

Any ideas as to what's causing this, and how it can be fixed?
I'll provide more information if needed.