it sounds like you have a signal light switch problem.
the brake light switch , goes through the signal light switch, then goes to the brake lights.
the reason why the brake lights are staying on, is usally because the hazzard switch ( 4 way lights ) is screwed up,( I have seen only rear brake lights flash when the switch was turned on or the front only flash ) .
when you depress the brake pedal and only one brake light comes on and the wiring and the bulb is good , this is an other indication that the signal light switch is bad.
the brake light fuse has power all the time. the fuse you are looking at mite be the antilock brake fuse.