Why does the handbrake light go on when I brake or when you are he road is uneven while driving (sudden movements)?
I thought it might have been the break fluid, but when I checked it was still full.
Since the brake (not break) fluid is still full, there is a problem elsewhere in the brake system. Please get it to a shop ASAP to have it checked out.
Same situation on my 99 Corolla last year. One of my steel brake lines going to the back wheels sprun a leak(corrosion) in one spot at the base of the firewall. Brake light will flash interminently at first. When the leak gets bigger,the brake light will stay on all the time.The pedal will sink to the floor and the car will barely stop.Check for a puddle of brake fluid under the car. Better get it fixed!
Handbrake adjustment needed or rear drum brakes need adjusting. No brake fluid involvement.