As per the schematic above the switch adds or removes resistance.
It could be thought of as a switch for higher output or lower output pickups commonly referred to as Les Paul or Strat settings although that analogy is based on your perspective. Maybe you just want less gain no matter?
I would expect your guitar to have high output pickups based on the critique of this circuit and the Blues Buster circuit in the other thread. This can easily be tested by plugging in a guitar cord to your guitar and testing the sleeve and tip of the other end with your Multi-Meter to get the readings from your pickups. I use vintage wound pickups always (all 8k or under) and easily get a wide variety of Drive & Clean tones. If your pickups read 10k output or higher I would not expect to easily achieve as many clean tones. The guitar essentially is part of the entire circuit.
If you find after testing the output of your pickups that they are vintage wound and you still have way too much Drive then it is likely a build issue and you should begin troubleshooting.
When closed, SW1 adds the resistance of R11 (1K) in parallel with the resistance of R10 (22K). This results in a parallel resistance of 957 Ohms. This resistance combined with the capacitance of C8 (220n) form a low pass filter. When the switch is open, the filter cutoff frequency is about 33 Hz. When the switch closes, the frequency changes to about 756 Hz The result is passing more bass frequencies when the switch is closed. Then the tone pot at P2 has more frequencies to act upon. I believe this is why Tonmann called this the Tone Centralizer because it moves the low pass filter closer toward the middle frequencies. I hope this helps.