That should have been done by the SAR officer in charge. First thing you do (or should) is drop a weighted buoy at the last known location.
In my opinion that wouldn't have proven very helpful. It took Mexico SAR over 24 hours to get the first asset in the air due to a lack of pilots or mechanical problems or whatever other excuse was used. Even if a dive op or SAR had dropped a weighted buoy that afternoon, unless it was enormous how would SAR spot it 24+ hours later by the time something could get in the air? Searching for it would prove as difficult as searching for a person. Maybe if it had a bright strobe attached that could help locate it at night and would be helpful but it becomes a very big ocean to search as hours pass due to the movement of the currents. I think about 72 hours later the possible drift patterns open up a search area almost the size of Texas... Flying across the state of Texas looking for something the size of a soccer ball isn't a good plan.
I still say the best course of action is to deploy an EPIRB as soon as a local 1 hour search or so does not locate the person. This could be a diver, snorkeler, or even someone swimming that went missing. Wherever that EPIRB floats it is broadcasting its pings to the satellites that are recording and relaying its location. Most EPIRBS broadcast 2 signals - one the satellites pick up that determine the general location of it via the Doppler effect and a 401 homing frequency SAR can pick up and fly to once they are within the general area identified by the satellites. Newer and more expensive EPIRBs have onboard GPS that broadcasts the exact Lat/Lon location to the Satellites. I truly believe if dive ops or SAR followed this practice as soon a 1-2 hour search does not locate the person, then, for up to 48-72 hours SAR is going to have a very good idea of where to search as the person floating should be in close proximity to the floating EPIRB as they are being carried in the same currents and generally subjected to the same surface wind conditions. No more screwing around with estimated current speeds and charts, wind calculations, etc. etc.
I would like to know if the U.S. Coast Guard would involve its assets in a search down by Mexico or if they are restricted or limited to SAR within a certain distance from US shores (after all, they are called the U.S. Coast Guard and it is not their duty to perform SAR off the coast of a foreign nation even for a U.S. citizen). I assume they are limited and that means rescue relies on the assets Mexico has to deploy which in this instance obviously demonstrated they are slow to mobilize, with undependable assets and pilots.
I spoke with a friend in Coz who informed me the dive community has and will continue to bring attention to how this was handled early on by Mexican SAR and hopefully something positive will come out of this incident... Like maybe Mexico SAR gets it assets in working order, has pilots on hand, and can react with a much faster response time. What would happen if a cruise ship sank quickly off the coast, 1000's of passengers and crew went in the water and it took Mexican SAR over a day to get a helicopter to the scene? Something tells me it would be an international horror story for Mexican authorities that would draw worldwide criticism but 1 diver disappearing... oh well... just another diver lost nothing to worry about. BUT Cameron's incident has made the news in a pretty big way and has drawn attention to their obvious SAR inadequacies. I was pleased to hear the governor of Q Roo contributed his private helicopter to the search and tried to make up for national inadequacies out of his control as best he could.
I apologize for this rant but if Cameron isn't rescued something positive needs to come of this that can save the lives of others who could be lost and floating at sea.