Yes, an external sync can be used to control the integration start time of the Tau SWIR. This can be used for events such as starting to image a scene when it is known that a laser pulse will be present. This also determines when a frame is output from the camera, and it requires a sync signal for the start of every frame.
If the Tau SWIR is not syncing to a very short event like a laser pulse, then the camera should operate in its normal free run mode. In this mode, the camera is outputting frames at whatever rate the user sets, between 1 fps to 60 fps. The integration period should be set to match the scene brightness that is being imaging. In this mode, the camera is outputting frames as soon as it is powered up (5s from power to imagery) and then outputs frames at the rate set by the user.
Note that the Tau SWIR camera by itself does not capture or record any frames of data, it just generates them. If a customer wants to start a recording of images, that capability would be in the software used for recording digital data. Some frame-grabbers include software for that purpose.