I have a 98 Civic and the brake lights wont go off. It appears the button behind the brake pedal broke because there is blue plastic on the floor. What is the part called that I need to replace?

 

Well since you did not mention your trim (CX, DX, EX, LX, etc.) & transmission (auto or manual), I cannot provide you with a part#.
But the part you need is called a SWITCH ASSY., STOP & CRUISE

 

Sorry, 1998 Civic LX 4 door 5 speed

 

It's not just that the rubber piece on the pedal arm cracked and fell out? That's what usually causes the brake lights to stay on. Press the button on the switch with your finger and see if the lights go out.

You can go to hondaautomotiveparts dot com and look at a diagram of all the parts with their names.

 

when mine fell out ^ i just bought a small bolt and a few washers and a nut 0.35$
to fit it.

 

When I press the button, the brake lights go off. Do I need to replace the whole switch?

 

No the switch is OK. You need to fix the rubber piece or make some substitute so the switch is pressed when the brake pedal is up.

 

I did a quick fix by epoxying 2 washers on the pedal arm to depress the switch.