When freezing a copper pipe with a refrigerant, how does one know when the pipe has enough ice to "cork" the pipe and halt water flow? Is there an indicator or a rule of thumb?
There are numerous water pipe freeze kits on the market. You can do a computer search for "water pipe freeze kits" or try "pipefreezekits.com". I however have never used a commercial freeze kit due to their cost. Instead of this method, I always used dry ice which was available at many ice plants. I have frozen water pipes up to 3" diameter in buildings. Since the size of the frozen pipe length is very short, and the discharge length was very long, there was never a chance for the pipe to burst.
How I did this was by using "shaved dry ice" put in a bath towel and wrapping the towel around the pipe using several outer wraps of the towel to act as insulation for the dry ice. Then you wait for the pipe to show an ice layer on the pipe just past the towel. As long as you maintain the dry ice the pipe will remain frozen. I once froze a 3" supply water line in a school where all the upstream valves would not close completely, including the utilities street shut off valve and kept it frozen for 10 hours.
Make sure that you protect any exposed skin and eyes with heavy work gloves and eye protection. The dry ice is unforgiving and will freeze skin and damage eyes in seconds.
Do a flow test. Water will no longer flow. Note that freezing water inside a copper pipe can easily damage it. The technique in the video could conceivably be useful in some complicated emergency situation that justified the risk, but valves are put at convenient locations in water lines for a reason, and if you find you really need a valve somewhere, you're probably better off shutting off the main and installing one than freezing a pipe.
Also note that copper is an excellent thermal conductor, so if you're thinking of freezing a pipe "just enough" its likely that your plug won't last very long and the moment the layer of ice touching the pipe melts, the pipe is typically straight and smooth enough to allow the plug to move down the pipe.