i had the same problem. my abs light would always turn on when i start the car and the abs module would buzz. i filled up the fluid many times becasuse it kept leaking every so often and after awhile it stopped leaking and the buzzing stopped too, but now my abs light just stays on. the light used to just go away after i filled it. i think its blown out or something.

also, if you listen closely to the inside of the car, near thermostat controls, like 5 sec after you start your car, theres a tick sound that caomes before my abs light comes on. it always happens. dont know what thats about either. i think its just the ecu or something sending the signal that theres something wrong.