If the Accord is like the Civic is ( and I had the SAME issue on a 88 Civic and 95 Civic ) the brake pedal has a tab coming off of it near the top. This tab pushes a PIN on an electronic switch ** IN ** turning off the brake lights. ( Its kind of backwards if you ask me ). What has happened to me twice is the TAB on the pedal has a plastic plug that breaks over time. It is clipped into a hole in the TAB on the brake pedal. Over time this piece of plastic will break ( and you may find an odd small ½" round plastic part in the floorboard ). Long story short, to fix this all you need is about a ½" to 3/4" long nut and bolt...about a 10mm I think will work. Put the bolt through the hole and put the nut on it. You dont want something with a big bolt head, I found a flatter rounded bolt works good and you want the bolt head to press the switch in when its mounted. I know this might be confusing, crawl under there and look at the pedal, if you see the switch that the pedal is supposed to push ** IN ** when released and a tab on the pedal with a hole in it that lines up with the switch then you will know thats what it is. Its pretty self explanatory and EASY to fix. If this is it, its not a bad switch or anything electrical, its just that stupid broken plastic tab.

REMINDER though that this is the way a Civic is built, I cannot say or verify if an Accord has the same functionality...but hey, we are talking about Honda right? SO MUCH of what they do follows the same functionality so you might be good.