When in pedestrian mode, the E and Q keys are inoperative, they move forward and back. Not up and down.
I would expect that they should allow you to move vertically until you land on a solid surface again. If you move up above a floor and let go of the key, it should land you back down on that floor. If you go below your current floor, it should land you on the nearest floor below the current, or take you to the other side of the earth.
If it is confusing to use the vertical keys in pedestrian mode, perhaps a modifier key should activate them, like Shift+E or Q, or Alt, etc.