The tube at the top of the brake pedal has plastic bushings in it where it pivots on the clutch pedal shaft (which also has the same plastic bushings where it passes through both sides of the pedal support); if those bushings are worn (and most are), the pedal will have the lateral slop you noted. You'll need to remove the steering column and the pedal support assembly in order to change/lube the bushings. Change all four, not just the two on the brake pedal - they're cheap. See your assembly manual, Section 5, sheet A3. Photo below is a Corvette, but the assembly is similar.