The lateral motion is guided with the use of ball bearing drawer sliders found at the home improvement store. These are available in a number of strokes, so a suitable one was easily found (16″).
In the picture above, there are two drawer sliders mounted to the layout. The upper one is for the Staging Elevator, the lower is for my Staging Fiddle Yard (for the passenger/express side). The Staging Elevator is coupled to its slider. The other slider shows a 1×2 beam with half of the coupling attached on either end. Between the Staging Elevator and layout, I have 1/16″ gap for movement. The ends of the model railroad tracks are flush to the ends of the layout and elevator so that they do not collide with each other when moving the elevator laterally. The sliders allow some movement so that this 1/16″ gap can be made smaller as the tracks are aligned. If the rails collide, a short in the DCC system will result, so I had to make sure they were at least flush, but not too much clearance as a bigger rail gap will make it more difficult to move the locomotives and trains on and off staging.
The ends of the rails are soldered securely to the tops of brass flathead screws screwed into the benchwork of the layout and staging. It doesn’t take much to rip a rail out inadvertently, like with a sleeve of one’s shirt.
The coupling above is actually from my Staging Fiddle Yard, but it is the same as used on the Staging Elevator. It is simply a door hinge with the middle loop cut away on the elevator hinge, while the mating piece is a smaller loop section cut out from the other hinge half. This provides for lots of vertical play, or forgiveness, for mounting and operating. The pin pulls out to separate the Staging elevator from the layout.
As I mentioned, this end of the elevator sits off the floor about 1/4″ so the end of the elevator needs to be lifted up that amount and placed on the horizontal beam (via the block on the silver wheel bracket). Then the coupling can be made to the drawer sliders.