Tech A says that mismatched tires may cause the ABS system to register a fault code. Tech B says that a TCS may automatically apply brake pressure to a wheel brake unit even if the vehicle is not being braked. Who is correct?

Tech A is correct

Step-by-step explanation:

Mismatched tires could activate the Antilock Braking System (ABS) indicator light because their rotational wheel speed could be dissimilar due to slight variations of tire size between different manufacturers and/or tread patterns. The ABS control module does have a fault memory and the ability to store fault codes.

A wheel speed sensor is the most common failure in the ABS system. The reason your engine management and traction control light are also on is because those systems "borrow" wheel speed information from the ABS system. The reason the fail so often is because they live in a hostile environment.

Traction Control System (TCS) allows brake actuation pressure to be generated to brake a driven wheel to prevent it spinning when peak adhesion has been lost during acceleration, and thus maintain traction by transferring the drive torque to another drive wheel that does have full adhesion.

In modern vehicles, traction-control systems utilize the same wheel-speed sensors employed by the antilock braking system. Traction control does not have the ability to increase traction; it just attempts to prevent a vehicle's wheels from spinning.

On the other hand, brake-only systems do appear to improve acceleration. It's important to remember that traction control does not affect the vehicle's ability to slow or stop in the event of a loss of control and potential crash; in short, it doesn't prevent crashes.