It sounds like the main side mounted brake lights are not working, but the turn signals, tail (running) lights work, and the center high mounted stop light still works.
The rear combination lights have three sections. The bottom section is red, but it is just a reflector, it doesn't have a light bulb in it. The middle section is yellow, it serves as the turn signal and the hazard light. It has a single filament #7440 bulb. The top section is red and has the dual purpose of tail light and brake light, it takes a dual filament #7443 bulb. This dual filament bulb has one filament/element/wire that lights up bright for the brake light, and a second filament/element/wire that lights up not as bright for the tail light.
Odds are that since the center high mounted stop light still works, things up front in the car are ok, and it is just that the brake light filament has burned out in both the rear #7443 bulbs. That's at least the cheapest and easiest first thing to try, replace the brake light bulbs and see if the problem persists. It is more likely that only one filament in a dual filament bulb burns out, compared to the odds of having both burn out at the same time
Electrically, there is no fuse or relay that would affect the side brake lights and leave the center brake light still working. Its possible that somewhere in the back end of the car the wires to the side brake lights are damaged, but nobody's had that and lots have had bulbs burn out
None of that solves your cruise control problem though