It is possible that one of the bulbs is shorting out. Try replacing the brake light bulbs, if that doesn't work, troubleshoot the brake light switch.
You probably have rusty/scored brake rotors.
Bad ground in brake light circuit
It's probably your brake lights, not your brakes.
excessive shaking when applying brakes points to brake rotars being out of round, cracked or warped. have rotors machined
Check the level of brake fluid in the master cylinder reservoir. If it is low that will illuminate the brake light also. If it is low on brake fluid it's time to have the brakes serviced.
If it is the clip I believe you are describing that comes in a hardware kit on drum brakes it is crimped on the emergency brake lever to hold it to the shoe.
Power brake booster is going bad. wont hold vacuum for power brakes to work.
Take your foot off the brake
A brake system brakes.
pad brakes are disc brakes, it's known as changing brake pads for disc setup and changing brake shoes with drum brake setup.
Brake rotors are warped.
The 1998 Chevy Corvette parking brake can be adjusted with the parking brake adjustment bolt. You can also adjust the parking brake cable.