I've never looked at the switch on a Z before, but I know that in many (most?) cars, the switch is a normal closed switch. When you push the brake pedal, it allows the switch to close (Your brake lights go on.). When you release the brake pedal, the arm pushes on the switch to open it. If the switch moves or breaks, it stays closed, and your brake lights stay on.
Does the 83 brake pedal have the same nylon/plastic bumpers for the switch as the later Z's? If so, you probably lost/broke them and just need to get new ones, or put a bolt in the hole that will contact the brake light switch. No biggie.