That depends on how you want to turn it off. I am not familiar with the Instron Fast Track, but the Eurotherm can be controlled directly from Labview using the modbus comms. When the test is finished, you can send a reset program command(if a program is running), or send a different setpoint, etc.
If you have digital outputs available on your computer, you could wire one of them to a digital input on the 2604 to do just about anything.
If you have the OPC version of Eurotherm iTools, you can control the 2604 with Datasocket connections.
Please give a few more details, and maybe we can figure out the best way to do it.