Brake lights do not turn on after changing light bulbs?

You can try some electronics terminal spray, I use it for corroded connectors, places where you see either white or green corrosion. Thats an indication of moisture getting into the connection. Deoxit is supposed to be the best, but they have a bunch of different kinds at AutoZone or advanced auto type places, wd-40 also makes a good terminal spray. Thats what I've been using. Spray the connectors and pins, let it dry out good.
Did you see any corrosion inside the harness connector?

Really. Well, that was definitely the strange one for the month. Glad you got it straightened out, I would keep an eye out on the whole lamp assembly, if you notice any moisture on the inside of the housing after it rains, then that will need to be addressed. Or you will keep running into the same issues over and over. There are a couple of Technical Service Bulletins I came across having to do with condensation inside lamp assemblies Ill post below. Along with 3 Recalls, the 1st one is that pad for the brake pedal, and I don't think the other 2 pertain to your vehicle unless you live in California (second diagram) and the other is for a Korea Built vehicle (diagrams 3 and 4). Diagrams 5 and 6, and then 7 and 8 are the TSBs for condensation in the lamp assemblies. Just wanted you to have that information.