Hi there Dylan, did you note this...
"If you want to run the Control module in a 3-wire connection (RXD, TXD, and GND), without remote
controlled activation, Jumper 5 (JP5) must be closed. This connects DSR and DTR together."
Just to be sure you do have the module configured correctly for 3 wire operation, it would be a good idea to isolate all other signals electrically and try again with the pc to make sure the module is in fact configured correctly for operation in this mode.