2006 Saturn Vue AWD automatic (not a hybrid) has a quick vibrating pulse in the brake pedal when applying the brakes. It is not rotor wobble (they have been replaced). It finishes with a load horn like vacuum noise and then a few seconds of ticking noise. The brakes work fine as far as stopping the car. Garage put it on a $10k test computer that found no error codes. He applied the brake pedal will the test computer was connected and then an ABS light came on on the dash for 2 seconds and then went out. His foot still on the pedal the ABS light came back on for another few seconds and went off. Still no error codes reported to the computer. He also found that all 4 wheel sensors were saying the wheels were rotating at 1 mile per hour (the car was stopped).

SOURCE: abs sensor

there is more than likely a piece of rust stuck to one of the front abs wheel speed sensors. this happens during brake service sometimes.

SOURCE: steering wheel vibrates when braking

i had the same problem in a 2001 avalon. i had the brakes machined and the problem was solved.

SOURCE: Brake pedal vibrates while braking and doesent stop right away

There's speed sensors at each wheel. You may have got some contamination in front of one of them... sounds like the abs is trying to compensate for un equal speed at each wheel... and something may be blocking a proper read at one of the wheels...

SOURCE: i have a 2004 saturn vue when i apply the brakes my abs comes on

It sounds like one of your wheel sensors isn't working, and the ABS is thinking that one wheel is locked up, so it's activating ABS.

SOURCE: 2002 Sayurn vue 3.0L

Under the intake manifold,  it will need to be removed.  Not too hard to do for the average diy but recommend buying a repair manual as a guide.  you will need a 1/4" drive T30 torx socket with a long extension one of the bolts is hidden but the others are under the black cover on the top of the intake.  you will also need to remove the coil pack held on with torx bolts.  8 or 10 inverted torx socket needed for that.