Chinese Adjustable 60W soldering iron problem
If the soldering iron is rated for 220 V and you're using it at 120 V then bypassing the temperature control circuit is useless. The control circuit will just apply maximum power to the iron until it has reached the desired temperature which in your case never happens.

A 220V 60 W iron will be around 800 ohms (measure that !) so at 120 V it will consume a power of 18 Watt. For an iron with a very small tip that might be enough but for a 60 W rated iron it's not enough power.

The Thyristor does not output 60 W, it SWITCHES 60 W. A proper thyristor will dissipate maybe 1 W (probably much less) in this situation.

60 W at 240 V gives a current of 270 mA, you don't need wide copper traces for that.