You can't do what you want directly, i.e. there is no mode that says just log the time stamps. I would probably use the FramesAcquiredFcn to get the time stamp and then discard the image data. You can store the time stamp in the UserData property of the videoinput object for later use.
For example:
vid = videoinput(...);
vid.FramesAcquiredFcnCount = 1;
vid.FramesACquiredFcn = @myFunction;
start(vid)
Your myFunction callback would look something like:
function myFunction (vid, ~)
[~, ts] = getdata(vid, 1);
timestamps = vid.UserData;
timestamps(end+1) = ts;
vid.UserData = timestamps;
