If you're talking about your Mazda 6, then the On/Off button is just for arming/disarming the cruise control, and is not dependant on the brake, so your mechanic is wrong and this may be related to the brake light switch.
My Mazda 3 has two light indicators for cruise control, your 6 should be the same, one is called "Cruise Main" and is activated by the On/Off switch, it will remain on, no matter if the cruise is actually engaged or not, pressing the brake pedal will not turn this light off either. Then there is the "Cruise" light that comes on only if the cruise is actually engaged and will shut off if the cancel button or brake pedal is pressed.
If “Cruise” light never comes on when trying to engage cruise, then the brake switch is likely the cause, especially if cruise was functioning properly prior to switch replacement. Also I think your mechanic is just being lazy, because the first rule of troubleshooting is to check the last thing you changed that might be related to the problem, and the brake light switch is directly linked to cruise control operation, instead of dismissing it out right.