I should have asked this question ages ago.
Do you read in the direction of the arrow? Is the current stage the one on the far left or far right? What if it's in the middle?
Am I totally wrong? Do the little icons even move around?
Because It seems like what I think it supposed to be next is never what I want when I go down to the mid towns.
Remember when the developers actually cared about making the arcade AWESOME? Have a seat...
The clockworks are made of giant rotating disks. Each disk contains a set of levels, and the direction the disk is rotating in is displayed by those arrows you're asking about. Your next level is the one that is directly underneath of your disk, provided the elevator is done coupling itself properly-- which is why the line going down occasionally has a sort of zigzag in the middle of it.
Because of this rotation mechanic, the waiting time between disks is dependent on the speed each disk is rotating at.. and each disk is indeed assigned a different rotation speed; for instance, some missions cycle very. very. very. slowly. This also means that the next level you see is dependent on which level you're already on. Imagine two identical disks, with a clockwork tunnels and a compounds, each at the same position. If I go down on one side of the disk to a clockwork tunnels from a clockwork tunnels, then a player on the other side of the disk in a compounds level would still be on the other side of the disk when they went down-- their next level would be compounds. COOLEST THING EVER if you ask me.
Random level rotations however are in fact random, and do not appear to rely on the rotation mechanic, at least when going down to them.