Check the ABS sensors and be sure they're clean, intact, and connected
properly.

-Russ.

Somebody says to check the sensors, this is always good, but I do not think
it is your trouble.

It sounds to me like your ABS is activating any time you use the brakes and
the ABS light is off. This is not normal operation, and the ABS system
eventually figures out that it is doing stuff that it hasn't been asked to
do - this is a fault that sets the ABS light on. When the ABS light is on,
the ABS system is DISABLED, and you then feel the brakes working normally.
The trouble is, they are working the same way automotive brakes worked in
the '60s, the brakes can make the tires lock and this can put you into a
skid.

HERE IS WHAT ABS IS SUPPOSED TO DO WHEN IT IS WORKING RIGHT
When you step on the brake for a normal stop, approaching slower moving
cars, stop signs, entrance to the liquor store, whatever, the brakes stop
the car smoothly and evenly.

If you are doing any sort of panic stop, hauling the car down from freeway
speeds to a stop in a very short distance, or even a normal stop but there
is ice on the road, one or more tires might lock up and skid. This is where
the ABS kicks in.

It will automatically release then reapply the braking pressure to that (or
those) tire(s) several times per second to maximize the braking process AND
let you retain steering control and directional stability of your car. There
is considerable argument that it can shorten or lengthen the overall
stopping distance, but there is no argument that the car can be steered
under full braking if the car has ABS and the ABS is working.

The ABS is a system that can not fix itself once it has detected an error in
its operation. That is, the car is turned on and the ABS does a self test
and the ABS light goes out. The system constantly moniters itself, and if it
detects an error, it will shut down and revert to the same braking
capability that was available before ABS was ever used. There can be errors
with the sensors that tell the system the tires have stopped turning, and
there can be an error in the valve body that controls the pulsating feeling
you report. The valve body costs in the neighborhood of $1500 to replace. I
said the system can not fix itself, this is true but deserves deeper
exploration. When the engine is shut off then back on again, the self test
repeats and the trouble might not be detected again until the brakes are
used or the car begins moving. Any error in the ABS system will turn the ABS
light on.

If the ABS light comes on when the car begins moving, or soon afterward or
an any time that is not related to actually using the brakes, then the odds
favor one or more wheel sensors not functioning properly. If the ABS light
comes on after using the brakes and there is a pulsating feeling (little man
hammering on the pedal) and you have no reason to think the ABS should have
kicked in, then you have trouble with the ABS controller or the valve body.

When the ABS light is ON, the ABS system is disabled. The brakes still work
fine, but the ABS feature will not be there and you should operate your car
accordingly. Do not engage in behaviors that can result in skidding, if you
drive on snow and ice, then do not expect to be able to steer if you need to
stop quickly.