First glad that the issue was resolved so you were able to continue on your trip home. Now to find your problem, with the information given of the brake light being on would lead to this. From the service manual 12.8 volts is required for the elecrical system to work, Your battery in the off position showed a reading 12.6 to 13.0 with it decreasing over time,all night. That being the case It would indicate a cell going bad than with the brake light staying on it brought the battery voltage down enough so the electronics do not to work properly, The electronics are very sentive to voltage change and require their minium to work correctly, if less than minium you get intermitten operation and heat build up and electric failure in one of your components not knowing which one. That is why it is important that for the battery always to perform to the voltage specifications with in the voltage range that is required by the tech manual for the components. I replace mine every three years. Maybe a good practice when one goes on a trip and the battery is nearing its useful life would be to take a new battery along with them, just in case, then you do not have to buy a $200.00 battery.
How about inatalling the new LED lights and/or new led bulb replacement?
The weakest link and most problems usually are the electronics/electrical
Could this be answer to the problem most likely= New battery