The elevator is located immediately to the right of the starting gate in the wall under the torch. But for some reason, the doors to it do not open, even if you run to the upper intersection with a moving bridge. There is an exit from this elevator. This is the starting room of the cropped map version. I didn’t figure out how to open it. I didn’t find any additional buttons. I was able to enter and exit the elevator using the “noclip” command.
It’s part of the original e2m10.map. The (fairly slow-moving) elevator is intended for deathmatch and blocked off by two func_wall entities on singleplayer mode, but it can be useful for coop as well. It now becomes accessible once you press the button that raises the stairs in the first area after the water hub room. The first step of the raising stair bridge killtargets the two func_wall entities (“t93”); just a simple hack, no classnames were changed.