What does it mean when my brake lamp light comes on in my 1999 honda accord 4 cylinder

Majdi, if you mean the brake warning light in the dash is on after starting your car, the light is telling you there is a fault/problem with the braking system. You should not continue to drive if the brake warning light is on, as your brakes could fail. You will have to have a good shop check your brakes and diagnose problem and estimate repair. Check the attached links,instruction and guides, Good luck
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Brake lamp warning light Honda Tech
Parking Brake Warning Light
What Causes the Brake Warning Light to Come on
http://honda-tech.com/honda-accord-1990-2002-2/%22brake-lamp%22-light-went-meaning-problem-1723211

The brake lamp light simply means one of your brake lights is burned out and the battery light means your alternator is not producing the proper voltage and/or amps to correctly charge the battery.

If you mean running lights (not brake lights) check fuses first, then bulbs, wiring connection in trunk, light switch. If you mean brake lights, check fuses, brake switch at brake pedal, grounds at lamps, bulbs.

great question. (running engine , no less)
1: that means the lamps in the brakes (3amps?) is overloading
a 50amp Alternator. (impossible nearly) but ???
or
wiring errors.
loose battery connections
shorted brake lamps or wires to same.
id the wrong size fuse in the brake fuse box.? if yes, you risk fire.

did you try all other accessories, on car, to see if too, overloads
the alternator (loose belt?O)
1: head lights.
2: cab heater fan on max
3: defrost heater in rear of car window.
4: all at onces?

if ONLY brakes? DO IT?, then remove all brake lamps. now.
and re test. brakes. no lamps.

all answers for a stock car, if car is hacked, all my answers are useless. (hacking is infinite) (alarm hacks, remote start hacks, cruise hacks. are common and a PITA)

You can try to replace all the brake lamp bulbs as sometimes eventhough all bulbs are working but one of them is about to blow and give high resistance. That's why the brake lamp lights up.

Brake switch possibly, Or an unrelated problem, the neutral safety switch. both cam be problematic with 1999-2004 hondas.

I assume you mean the one on the dash. This is an indicator that there is a problem in your braking system. Make sure it's not low on Brake fluid and have the brake system checked or check it yourself. If your going to check it yourself I recommend the Haynes repair manual on your vehicle as a reference.

The back brakes on my Honda Accord are disc brakes. After removing the brake cylinder assembly you will see the brake cylinder piston end has a slot in it. The short pin on the back side of the inner brake pad fits into this slot, but also it is used to 'Turn' (clock-wise) the piston back into the cylinder so you fit the assembly back over the new 'thicker' pads. You can not 'press' this piston back into the cylinder.