The cruise control won't work if the brake light switch or brake lamp circuit is open-circuited. When you press down on the brake pedal the switch opens the cruise control circuit and the cruise cuts out as it would obviously be unsafe for the cruise control to try to maintain the vehicle speed while you're trying to slow the vehicle down while braking.so the cruise and the brake problem are related. They do have the brake switch (found under the dash at the top of the brake pedal) in common.The issue with the brake lights being on when the headlights are on means they are getting power from somewhere when they shouldn't. That place they shouldn't is probably through the brake lamp switch circuit. The circuit is complete when the brake lights are ON. when the brakes are not applied the circuit should be open. You problem is that the power from the tailights is not running to ground but rather back through the brake lamp circuit in search of a ground. When you close the brake light switch you enable the ground for the brake lights so the lights get brighter operating as they should and that prohibits the taillights from using a powered circuit for ground. Hope that's not too confusing.I recommend you check the ground wires for your taillamp bulbs. They should be in the left rear corner of the trunk under the trunk mat or against the taillight panel. The grounds are usually black wires that run from one of the brake lamp sockets to the metal of the car body somewhere inside the trunk near the taillights. I think you're going to find one of those ground wires is loose or broken.if you find them intact, my next suspect would be the brake lamp switch. Let me know what you find out with the ground and if its not that I'll do some more research.hope that helps