Most pad sets are now provided with vibration damping shims that fit between the back of the pad and the caliper. If shims are present, additional Brake Quite, by itself, won't help much.
Another aspect that is often involved, is that the pad backing plates wear groves in the caliper where the pad backing plate lower ends touch the machined pad support surfaces of the calipers. The grooved pad supports, prevent the pads from sliding freely on the caliper pad support. This will cause the pads to hang up more or less, and the hang up will cause uneven pressure on the pads against the rotors. This is frequently the cause of squealing brakes. Fileing or better, machining the caliper pad supports to eliminate the groves, is an important part of relining brakes, and will help prevent the vibrations of the pads that cause the squealing noise. There is a limit to how much material can be filed or machined away without wrecking the calipers obviously. 1-2 mm is OK, but more than 2 mm would mean welding and re machining or replacement of the calipers. Stainless steel shims at the lower and upper pad supports is also a pr oven fix for wear groves in the calipers, but is a custom fit solution.
Finally, lubrication of the ends of the pad backing plates and adjacent pad support surfaces, using synthetic high temp disk brake caliper grease, is also highly effective helping to prevent brake noise, but is only helpful if the calipers have nil or no backing plate wear groves.
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