A button at the top floor sends a signal to a T flip-flop which toggles power/no power to the gearbox immediately adjacent to the pulley. The button also sends a signal to a monostable circuit which temporarily disengages the brake (AND gate with a detector) so that the elevator can descend from the top floor. At the bottom floor, there is another button. it sends a signal through a 2x2 redstone staircase up to the top (one repeater needed to lengthen signal) where it sends a signal into the same circuit that the top floor button does. I'm not sure as to the exact terminology here, but that should become clear - I hope - in the photographs.
Now, this works perfectly fine in most cases. When the elevator is at the top, pressing the button at the top makes it descend. And when the elevator is at the bottom, pressing either button makes it ascend. However, pressing the bottom button while the elevator is at the top does nothing except toggle redstone power to the T flip-flop. I'm sure this has something to do with delay and also with my braking system, but I'm not sure why the bottom button is not causing the brake to disengage.
Some pictures:
Elevator top floor
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Elevator bottom floor
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The monostable circuit that lengthens the time the brake is disengaged, allowing descent
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I apologise in advance for any grimaces you might get from looking at that, this is the first time I've ever made and used flip-flops and monostable circuits. It's by far the most complex thing I've made yet, and the bug is fairly small so I'm basically still proud of it.