I might suspect a BECM issue, but I would start with the less expensive stuff. The wiper is probably just the wiper handle. I've noticed that with mine, if I move it forward and then back with the vehicle off. It will actually turn on the next time I start the vehicle, but only cycle once. A malfunctioning switch in the handle could be causing this. The brake light, I honestly don't have a clue if its doing it while the vehicle is off. The ABS light will be on until you go about 5mph, then it will extinguish. That is normal operation, if it stays on, then you have an issue. You should just be able to pull codes from the vehicle using a standard OBD II scanner. How is your battery and alternator, these two items can cause some very awkward issues if not functioning properly.