Are you sure you're not losing vacuum? If the brake vacuum reservoir is getting all the vacuum bled out of it I could see that turning the light on... Have you tried barely pushing the brake pedal when the light comes on like that? If you had a stiff pedal that would be a good indicator...

It's brake fluid level.....

That light is, by design, supposed to come on when it thinks your brake fluid level is too low.

increased pressure in the system plus expanding brake lines would "compress" enough fluid or fill up the increased volume in the lines to make the sensor think the fluid level is low when it's just preoccupied in some other condition...

SS brake lines + more fluid/better fluid = solution!