Brake Light On problems of the 2010 Honda Insight

Unexpected acceleration when braking, this is a reoccurring problem. I was driving about the speed limit on secondary roads ~40 mph no traffic and the roads were clear of ice and snow and the engine was warm, the instrument panel indicator for cold engine had extinguished. I approached a red street light I press the brake pedal lightly, there were no cars in front of me (foot clearly not on the gas pedal) I expected the car come to a leisurely stop by coasting with little braking help. The brake pedal felt stiff, resisted the pressing of the foot. The engine began to rev up and I also noted the battery ima charge/assist gauge went higher into the blue (ima assist). I applied more pressure to the brake pedal the engine accelerated more and assist gauge increased further into the blue area. I repeat: the brake pedal feels hard like putting your foot on a rock, no give. I now know this is the first sign there is going to be a braking issue. It happened every time the problem occurs! but the problem did not occur every time I stopped on this trip. When I brake and the car and the car goes into auto-stop mode there is no issue. When the unexpected acceleration occurs I can shift the car out of drive (d) and into neutral (n) the engine will momentarily race, exceeding 5000 rpm, almost red lining, and then return to a normal idle. It should be noted that the problem persisted thought the trip with the car being shut off and parked for a short time (2 occurrences) restarted and driven again. Only when the car was left for hours including overnight did the problem go away, my guess is 19 hours.