Is there a notion of "requesting control" or other arbitration like calls that can be made in the API associated with the MIP SDK or is it just inherent in the PTZ calls themselves in that if the call does not work, the current user cannot have control?

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No. With the MIP SDK you can send a PTZ command, there is no feedback mechanism. If the camera is in control by another user or for some other reason is not capable of performing the command this information is not available in MIP.