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Testing hydraulic brakes for leaks primarily involves a careful inspection of the brake fluid itself, particularly looking for signs of leakage around the brake pads or shoes. When inspecting the brake components, any presence of brake fluid on the pads or shoes may indicate that there is a leak within the hydraulic system. This is critical because hydraulic brakes rely on brake fluid to create the necessary pressure to engage the brake pads against the rotors.

Identifying leaks is essential for ensuring the safe operation of the braking system. If the fluid levels drop due to a leak, it can lead to reduced braking effectiveness, potentially resulting in collisions or accidents. Thus, the observation of brake fluid on the pads or shoes serves as an important indicator that maintenance or repairs may be necessary to address the hydraulic brake system's integrity.

The other options listed do not specifically pertain to detecting hydraulic brake leaks: checking engine fluid levels pertains to vehicle performance but not directly to brake operation, monitoring tire pressure is crucial for vehicle handling but unrelated to brake function, and checking power steering fluid does not involve the braking system at all.