How's actually working mechanism of dual wattage soldering iron what's the extra wire, so total 3 wires, connected to the heated iron ?

 

How's actually working mechanism of dual wattage soldering iron what's the extra wire, so total 3 wires, connected to the heated iron ?

Typically it is a full power for one switch position and the other switch position runs the AC power through a single diode for a half-wave rectified supply to cut the power by half. .

 

The use of a diode does not require a third wire.
Just guessing: the soldering iron might be switching between heating elements or selecting between driving the full heating element or a shorter section of that element.

This can be tested with an ohmmeter.

 

I think it is a cheap soldering iron without any temperature control so when set at "High Power" and sits not soldering then it gets hotter and hotter until its tip and the solder are destroyed. The user is supposed to guess if it is too hot to solder then turn the switch to "Low Power" then wait and guess that its temperature is good.
When the switch is in "High Power" mode then it heats up faster.

Other cheap soldering irons have a light dimmer circuit to adjust the power then the user can guess where to set it.

My soldering iron has temperature control that heats up fast until it senses that its tiip is at the correct temperature then keeps it at that temperature.