FWIW, I had replaced by backup lights with LEDS, lic plate and inside lights, all with LEDS. Then I replaced the brake lights. I never really had driving the jeep for a long time at night but one night, I spent over 4 hours on the road. On my way home, i was at a stop light and could smell something burning. Thought it was brakes and the car in front of me. Down the road, next light, I still could smell it, just stronger. WTH!... Stopped in a parking lot, shut car off. Got out and walked around it. I could smell what seemed like a burning smell from the back of the jeep. OH NO... Well, I started it back up and was about 2 miles form home. Made it. My garage stunk like electrical fire all weekend (yep, put a lot of trust in my fire alarm system for the house but wife was freaked out I'd park my little 4x4 firepit inside). That monday, took it to the local mech. They found BOTH rear brake lights not working, one back up light was out also. They said my brake switch inside the jeep was FRIED. It looked like it was a little melted but enough to stink. Every time I turned on my heater, I could smell that burnt electrical smell. More like wire then circuit board. They put in standard bulbs and replaced the switch.
I did put LED backup lights back in. Figured if they were overheating, it wouldn't matter since they are not on that long anyway. I assumed that driving at night, the rear brake/parking lights might have got hot enough to short circuit and fry my brake switch. Wires seem intake from what I could see. So, not saying this was the LED's fault, but the electrical guy who fixed it said he's seen other cars do this when the lights would "fry", get hot and melt the switch instead of the brake light wires and running them for 4 hours strait could have caused it to overheat enough to melt the switch. We really don't know and I just keep sniffing for fire when I'm out at night (and I make sure my fire ext is in good working order).