I am not a mechanic, but, without delay, I would flush, not just drain your Honda's power steering! Brake fluid is engineered to operate at high pressure, high temperature in a sealed system. When exposed to the air it draws water like a sponge and is not a very good lubricant. As I remember brake fluid has an alcohol base.Power steering fluid circulates through the hydraulic section of the steering acting as both a lubricant for the pump and valves as well as an actuator. As I remember, power steering fluid has a mineral oil base. These fluids are designed to do a specific task in a specific environment. Brake fluid will harm your very expensive Honda power steering. Incidentally, Honda is very particular about using its own power steering fluid. Do not wait.