Don, you're really taking it on the chin here. I don't want to add to it but I hope you give some serious thought to a rescue course.
Most of what you'll learn is pretty common sense stuff but, common sense isn't so common especially when you have to think fast. You also get to practice applying what you learn in semi-realistic mock emergencies so when you have to do it for real it's not the first time you've done it at all.
Some key points you'll learn in a rescue class that might have helped here are things like...
Before beginning an in water search, take steps to be reasonable certain the person you're looking for is in the water.
ONLY send adequately trained divers with enough breathing gas and no-deco time (where applicable).
If there are other people around use them. Assign tasks. If you are the most qualified person on hand you may do better to stay on the surface to direct rescue efforts. Some one needs to run the show. Tasks that you might want to assign could include... activating EMS - most of us dive around civilization and response times are often like 7 minutes so in many cases you might not have to do anything else at all. Assign surface spotters and searchers even if there is also an underwater search. Have some one gather equipment that may be needed, Oxygen, ropes for searches, surface markers or whatever.
That's by no means everything but the intent is to put an organized effective search/rescue plan into action that above all else does not add to the problem by creating more victems.
Searches are one of the things you'll lear a little bit about in a rescue class.
It can be hard for a lone diver to conduct an effective search in OW in the first place especially without previous practice and the right equipment (lines, markers ect, depending on the topography and the size of the area to be searched). The diver is likely just swimming around wasting time.