Since you are making the fuse companies happy....have you looked at the "interlock" switch? It is an auto so there is the switch (neutral safety/interlock) inside the console by the shifter...have to press the brake to shift out of park? Also might look at dis-connceting the brake lamps (right, then left) at the connector in the trunk to see if the fuse keeps blowing.
Last one, is this a wagon or sedan? I ask because I saw a post of a wagon where there was water in the rear fender that was causing the same strange thing.

 

There was a recall done on 99 accords for the "interlock" and ignition switch... If one of those is your problem Honda should fix it for free as it was a recall done on those parts, im going next week to get my ignition switch replaced... car starts, sputters, then turns off.

 

Water in the lamp housing is a funny thing. Sometimes there's enough greasy oil around the base of the bulb, so it still works. Sorta. I'd get the water OUT first, just to see if that fixes it.

 

i had tha same problem talkd to a buddy that is a 10 year tech at a dealer 3 posibilitys
1 it could b a aftermarket brake light switch... he said nothing is compared to oem and to trust him
2 siliniod that releases the gear wen pressed on break is bad...
3 he said ur car is probly phyco then laughed... all i did is replaced siliniod and brake swithch didnt have time to guess and see witch one it was... but in mean time there is a qwick release button near ur shifter that u can plug til u figure it out so u can drive it...did that for a month