I was normally driving today and came to a stop on a turn off and all of a sudden my brake alarm (constant sound), ABS light, and parking brake light came on.

I parked the car to inspect everything and didn't see any brake fluid leaks or low brake fluid in the reservoir (it's at the max line).
No ABS codes popped up except for a P0770 and P0442 but they have been there for a year plus.

My brake pedal is still firm and stops normally and my ABS pump motor still kicks on and off normally. No weird sounds from the master cylinder either.

When I put my car into ACC ON position the alarm and lights turn off after a minute or so but when I drive the car the alarm and both lights come back on after 5-10 minutes.

Any ideas what could be causing this issue?

Your TC inst locking up code P0770
P0442 is evap leak .

Being when its moving it sounding like your VSC trac system is going crazy. IF the CEL is on it should be disabled the VSC TRAC lights should be on. Does the chirp or are the lights flashing?

Correct, VSC and TRAC lights are both on but have been for quite some time as I've had the P0770 since the tranny was rebuilt a couple years ago and have been fighting evap leaks for some time.

No lights are flashing, just the abs and brake light turning on with the subsequent constant brake alarm. Odd thing is, I have no brake fluid loss or trouble braking. Going to try and jump the OBD port in the engine bay and get the abs codes.

Interesting.. I unfortunately have nohting at the moment. :-(

Check fuses and tailgate wiring looms for shorts.