Re: Brake lights
This is a shot in the dark, as I don't have a CJ, however since you've already checked the brake light switch and mention that the hazards / flashers on the rear don't work either, I'd check to see if power is getting to the rear taillights. Possibly as simple as a fuse / bulbs, but could be wiring, bulb sockets, relays, etc.
Yea, I know... Not incredibly helpful, but a place to start. Grab a multimeter and see if you are even getting power back there and move on from there.
Best of luck!