well.......
I just had the problem of my brake lights being on all the time as well, whethter the car was on or off.....
Everyone thaught that it was my brake switch, but it was just the "grommet" it's a lil rubber piece that goes in a whole on the brake lever behind where the brake switch is so that when your not on the brake it pushes the switch and your tail lights turn off My car has 2switches that needs those

check to see if your Altima has one or two, and look where the brake switch button is in relation to your brake pedal lever, and if you see an empty whole, that means your missing the grommet.......look for it on your floor somewhere, they pop out after a while