We've had rotating walls, so now we need some shifting walls. A pair of gears linked to a single drive gear moves two L-shaped walls horizontally and in sync, allowing access to switch from NE-SW to NW-SE. The central chamber contains a door to a room with stairs down to another level (feel free to substitute a trapped chest or something else entirely, if that's inconvenient.) A secret room in the North has the control levers. There's also a room where the gears are visible, but it's not accessible from any of the rooms on this level of the geomorph. The only access noted is a staircase from a lower level.
There's no indication of what drives the gears in this case. Perhaps the drive gear is in turn driven by a set of gears linked all the way down to a large cavern where a chained dragon walks on a treadmill. Or perhaps there's an underground stream or wind tunnel.