1999 INtegra GS-R 4 Door

THe other day, someone on the highway pointed out to me that my taillights were out. When I go home, I replaced the fuses. The next day, my Dash Lights burned out. Replaced the fuses. I chalked this up to coincidence until it happened again.
Finally, I was pulling my car into my garage one night, and noticed that every time I hit the brake, it would be as if I turned the parking lights on. The corner lights, Dash lights and tail lights went on every time I hit the brake pedal. So I'm assuming that when I hit the brake while the lights are on, this is doubling the amount of Amps that the bulbs are supposed to handle, and thus burning the fuses out.
Can anyone suggest what could be cause=ing this problem?
Any help would be appreciated. Thanks.