How can I use the SMARTDAC+ GX/GP series' digital input module to start/stop recording with contact ON/OFF?

You can do this with an event action. For the settings, see section 1.19.2, “Event Action Setting Example" in the user’s manual.

Note that to operate a controller with contact ON/OFF, you must set the operation mode of the digital input module to Remote. For details, see section 1.11.3, “Setting the Operation Mode of a Module" in the user's manual.