It’s a standard 5.5mm x 2.1mm plug. I ordered a 26’ long cable that had the two wires separated more like a lamp cord to make it easier to splice.
Since I plan on mounting the relay control box just behind the plate marker on the gantry I then used the other half of this cable to extend the length of the Cutzilla wall plug cord.
Here are the LS torch fire plug and the new Amazon-bought Cutzilla On/Off plug.
Above is the new plug & cable spliced to the Cutzilla on/off connector (blue rings).