This is the full service manual for hypertherm’s sync torches.
It includes a lot of details including a good picture of the colors of the wires from the trigger switch.
Some of the information in this manual May shed some light on your situation.
I run a sync adapter so I don’t have the same torch.
And here is a link to the operator’s manual
And a link to the service manual
This service manual does have a lot of breakdown diagrams.
Edit.
But the very real and likely possibility remains that there will be some kind of software lock that’s looking to see whether the torch trigger is an open or closed position which is also tied to the CPC port.