Anti-lock brakes engaging when not needed

You need to have the ABS system scanned. You probably have a bad wheel speed sensor. most likely located in one of the hub bearings meaning; you may have to replace a hub wheel bearing assy with the faulty sensor. Traction control uses the same speed sensors as ABS. when the warning lights are on the system is not working.

you will need to bleed all four brake lines

the trac light is designed to come on to let you know that the traction control is working, it works by engaging the anti-lock brake system to keep the front wheels from spinning, it will also come on if you are stopping hard enough to engage the anti- lock brakes, this also could be a sign that your brakes are getting worn and might need replaced

Are there any malfunction lights coming on? If so then it could be a wheel speed sensor. sometimes people confuse rotor vibration with abs pulsation.

check and clean speed sensors, bleed brake system

Anti-Lock Control —Vehicles Built After 03/2002 The 3-channel anti-lock brake system consists of the following components:

• front wheel speed sensors
• front wheel speed sensor rings
• hydraulic control unit (HCU)
• Anti-lock brake control module (ECU)
• rear wheel speed sensor
• rear wheel speed sensor rings
• yellow anti-lock brake warning indicator

The 4-channel anti-lock brake system with traction control and stability assist system consists of the following components:

• active brake booster with integral solenoid
• brake booster release switch
• front wheel speed sensors
• front wheel speed sensor rings
• hydraulic control unit (HCU)
• stability assist module (ECU)
• stability assist event indicator
• lateral accelerometer
• longitudinal accelerometer (4x4)
• rear wheel speed sensors
• rear wheel speed sensor rings
• steering wheel position sensor
• yaw rate sensor
• yellow anti-lock brake warning indicator
• brake pressure transducer
• traction control switch

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I suspect the abs issue is causing the speed control not to work if it happened at the same time the cruise control stopped working. When the yellow ABS light comes on, it means the ABS is dactivated. You may have a faulty accelerometer which senses acceleration and yaw (side to side lean). I have not seen a bad one but you said it is sensitive to acceleration.
I would unplug it and see what happens. The connector should have a small tab to depress so you can pull the connector out.
Here is where it is:

Accelerometer Removal and Installation

1. NOTE: The accelerometer is located under the center, rear passenger seat carpet. (I think you have to remove seat for access).
   Cut the carpeting along the perforations.

1. Disconnect the electrical connector.

1. Remove the nuts and remove the accelerometer.

Have dealer hook up tester and pull fault codes if you can't find an easy solution.
Some background info

A malfunction in the anti-lock brake system will cause the anti-lock brake control module to shut off or inhibit the system. However, normal power-assisted braking remains.

Malfunctions are indicated by the yellow ABS warning indicator in the instrument cluster.

The anti-lock brake system is self-monitoring. When the ignition switch is turned to the RUN position, the anti-lock brake control module will carry out a preliminary self-check on the anti-lock electrical system indicated by a three-second illumination of the yellow ABS warning indicator in the instrument cluster.

During vehicle operation, including normal and anti-lock braking, the anti-lock brake control module monitors all electrical anti-lock functions and some hydraulic operations.

Each time the vehicle is driven, as soon as vehicle speed reaches approximately 20 km/h (12mph), the anti-lock brake control module turns on the pump motor for approximately one-half second. At this time, a mechanical noise may be heard. This is a normal function of the self-check by the anti-lock brake control module.

Pedal pulsation coupled with noise while braking on loose gravel, bumps, wet or snowy roads is normal and indicates correct functioning of the anti-lock brake system.

Warning Lamp Indicator
The anti-lock brake system (ABS) uses the yellow ABS warning indicator to alert the driver of a malfunctions in the ABS.
The yellow ABS warning indicator will come on to warn the driver that the ABS has been turned off due to a symptom that exists in the ABS. Normal power assist braking remains but wheels can lock during a panic stop while the yellow ABS warning indicator is illuminated.

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Please report back, I am curious if that is what it is. Good luck

sounds like the anti lock brakes are engaging are there lights coming on the dash at all???

that is what it is desgined to do - reduce acceleration and apply the brakes intermittently when the wheels spin. You have a switch you cn push to disable it. You need to disable each time you start car. See owner manual.

06-10: Traction Control 1996 Contour, Mystique Workshop Manual
DESCRIPTION AND OPERATION Traction Control System The optional traction control system is designed to control wheel spin when accelerating on slippery or loose surfaces. Traction control system is available only with anti-lock brakes. The traction control system includes the following components:

• Hydraulic control unit.
• Throttle control actuator (9N825).
• Traction control switch.
• Traction control warning indicator.
• Front brake anti-lock sensor (2C204).
• Rear brake anti-lock sensor (2C190).

The traction control system operates as follows:

• System functions by transferring torque from the spinning wheel to the wheel with the most traction.
• This is achieved by applying the brake at the spinning wheel through the hydraulic control unit or reducing the throttle opening.
• Traction control braking and throttle control occur at vehicle speeds up to 50 km/h (30 mph).
• At vehicle speeds above 50 km/h (30 mph), only throttle limiting control is used.
• If speed control is operating when traction control system engages the traction control system will disengage speed control through the use of a speed control relay. This action is the same as applying the brake pedal with speed control engaged.

1996 contour
Traction Control Switch The traction control switch is located on the instrument panel, left of the steering column.

First disconnect the negative battery terminal for about 15 min's. This resets the computer. Then drive it watch the dash for anything that illuminates. Connect a OBD2 reader to your obd2 port scan for codes. Troubleshoot your car. It really not that hard. Like following a line. Check your brake cpu unit. Get the car manual to. Check how to test the Brake module. If the voltage and ohms are correct. Go to the next part in line, electrically speaking. Find what input and output
location of the ALB system on the PCM (computer). determine what sensor is connected to the PCM and test them. If all ok. Look for a mechanical failure.