You could run a power wire from the towing vehicle and power the brake unit off of that.
The problem with leaving the power on is that it messes up the computer. You will get all kinds of lights. Just doing a battery connected short test tow with my Focus around the parking lot to test the tow bar out resulted in an ABS failure, a Hill Assist failure and a Check Engine Light for a transmission code. I had to pay the dealership to clear the codes. I was also told by the dealer that leaving the battery connected will cause the odometer to track the towed miles. Additionally, leaving the power on will likely result in a dead battery.
I don't use a brake unit and I disconnect the positive terminal. I wired my flat four trailer connector into factory light harness using diodes from Radio Shack ($1.35 a pair) to keep from powering the electrical system with my blinkers. I have towed my Focus from South Carolina to California to Washington to Virginia and have not had a single problem. I've even had a deer cause me to jack the brakes and I had no problem stopping. I know that what I am doing is not conventional, but it works safely and legally.
RK