New info: the problem seem to be related to the slope of the car rather than the amount of throttle. For example 75% throttle on flat ground would cause it to happen, but just enough throttle to move the car on a steep hill also sets it off. Braking and sloping the car the other way makes both lights go away.

Also it isn't just the parking brake light coming on. The "Trac Off" light is also coming on and off simultaneously with the brake light.