Where are the switches, and what do they do?

I found two switches in the corner of the map. They appear to switch from right to left when I approach them. I imagine it's not a coincidence. How many are there, where do they spawn, and what are they for?

Solution 1:

There are multiple versions of this puzzle, one for each overworld: switches, blue buttons, and green buttons. I believe the first is the main/primary overworld, as it's where everyone starts. You have a chance of changing overworlds upon each return to the town (not sure if changing towns is random or after spending a certain amount of time in the overworld, etc.) If you reset overworlds, your switches are reset and you can start over. You can do the switch puzzle as many times as you want on each overworld.

Switches

In the main/original overworld, activate six switches (by moving near them) to be transported to another island and receive the "Time Hammer" weapon and the "Something Switchy Going On" achievement. This can be performed multiple times. If a switch doesn't flip to the left when you approach it, you may need to visit another switch and come back (most likely a bug and not a need to visit switches in a specific order).

I'll list the switches in clockwise position:

1. Due north of the town, in the haunted area (south of the ice area).

2. Northeast of the town, in the candy area (follow the river).

3. Far east of the town, in the circuitboard area.

4. Southeast of the town, in the forest area (to the right of the toilet statue).

5. Southwest of the town (due west from the last one), in the desert area.

6. Farther southwest of the town (due west from the last one), past the desert area. Look for the cup of water as a point of reference.

You'll be immediately transported to an island. Take the new weapon before flipping the switches to leave!

Green buttons on white Ionic pedestals

To identify your overworld map, note the desert to the north (I also noticed a few Greco-Roman house around, but not sure whether it's an indicator):

1. Northeast of town, in the elite/siren desert area, just south of the northernmost haunted area:
2. Southeast of town, past candy land:
3. Far south of town, in the forest:
4. Slightly southwest of town, along the river and near the picnic:
5. West of town, past the graveyard:
6. Northwest of town, near the pearly gates:

The secret area has a dinosaur head:

Blue buttons on black pedestals

To identify your overworld map, note the rivers:

1. Far north of the town, in the birthday candle maze:
2. Far east of town, in the arid area with spikes:
3. Far southeast, near the cluster of coins and ziggurat of question marks:
4. Just southwest of town, in a valley with a waterfall:
5. Far southwest corner, near the holes in the ground:
6. Far west of town, past the haunted area:

The secret area has dad's axes: