First of all, my brakes seem to work properly! Brake light on my dash comes on when I accelerate. Only after a complete stop. Usuallly around 3000rpm. All pads,shoes, and fluid level are good and no leaks in the brake system. The light then goes out.
It could help to know the make, model, and year of your mystery vehicle with the flickering brake system warning light.
AFAIK, there are mainly two kinds of brake warning systems. One is keyed off of pressure differential between the front and back brakes, and the other is keyed off of brake fluid level in the master cylinder reservoir.
Yours must be the latter kind, because the differential kind will only first trigger the light when you are braking. You say that the light comes on while accelerating. That fits with a low brake fluid level, or maybe bad float switch.
Recheck the level, and try adding just a little even if you think it is full. If the light stops, then you’ll know. It’s time to check the pads then to see if they are worn down, or to look for fluid leaks.
1989 Toyota celica w/ 3sfe. I did check fluid level (actually bled the system) and float switch. All seem to working fine.
IIRC, in some Toyotas the brake system warning light could also light up when something is going wrong in the charging system. Someone with a good mind for schematic diagrams of auto electrics maybe can explain this better than I can!
Do you have ABS? Do you have a separate ABS light? If the ABS has a problem, such as a bad wheel sensor, and if you don’t have a separate light for ABS, that could set a light. Check your owner’s manual. I assume the brake light comes on if you pull on the parking brake while the car is running? You could have something as simple as a loose microswitch, or you could have a sticking emergency brake that remains partly on even when the handle is released.