I just dealt with this last winter. Turns out the the brake light switch just needed to be re-adjusted. Apparently there is a point where the switch will not activate the lights, but will kick off the cruise control. Obviously if you tap the brake pedal, the cruise control will turn off. The switch is pretty sensitive I found out, and it took my wife and myself to get it adjusted properly. Let me explain, if adjusted too far out, you can actually be stopped say at a stop sign or light, and if you are only lightly pressing the pedal to hold the vehicle in stopped position, the brakes may be activated enough to hold the vehicle, but the pedal may not be depressed enough to activate the switch to energize the brake lights, I found this out by adjusting the switch too far out initially. Therefore I was under the dash a lot with my wife watching the rear of the vehicle to make sure the lights would activate when I would press the pedal by hand, with light to moderate effort. A couple of test drives in between to check the cruise issue and voila! no more shut-off. Not difficult at all if you have just a bit of mechanical know how, you just have to take your time and be patient (even though in reality it only took about 15-20 minutes to fix, at no cost). It only took 1/4 to 1/2 turn on the shaft to get it to stop activation of the brake light switch while driving down the road. Have had zero problems since this adjustment.
I too have 268K on the Tree, we use the vehicle as an overlander and have put many miles off road, which I suspect is the reason the brake switch began acting up due to all the bouncing about.
I hope this post helps you and others deal with this frustrating issue effectively.
