Once you've messed with awakening Goal, you'll be able to return to the Assembly Hall to find the mayor asleep. Collect the clock on his neck and use it at the visitor's desk in the Town Hall to open the post office. As soon as you enter, you'll see on the left screen another doorway leading up to the Operator's platform. This will be where the puzzle is located. Return to the Mayor's room and unlock his bed in the drawer, then look under the pillow to find the planet's magnetic field. At the operator's platform is a fuse box near the pigeons that is strangely empty. Put the field machine in here and then mess with it.
The goal is to, for some reason (not clearly described when I was playing) make it so the middle column only has one lit-up bubble to it. Look at the device as if it were a phone, with 1-2-3 on the top, 4-5-6 on the middle, 7-8-9 on the bottom, and 0 at the very bottom on its own.
Using the phone layout, operate the dials itself to dial: 6 5 5 4 5 5 6 5 5 8
If you have to, back out after you've made the middle column show only one. The bars at the top help you keep track of this.