Breaking news - My rear brake lamp warning light had been shining in my face, so I took my car to my favorite mechanic. Upon examining the pigtails, he discovered that one of the two contacts ("nubs") in one of the sockets (pigtails) was broken off and therefore the bulb would not make contact, and also that another pigtail had been replaced at some point years ago by a previous owner, who had used butt-end connectors to connect the pigtail he installed. He also discovered that the third brake light wire from the car to the trunk (front left corner of trunk lid) was chafing and making an intermittent contact.
My mechanic was able to obtain a new pigtail at an auto parts store (Honda would only sell a taillight wiring harness for $$$) and solder in the new connector, plus cut out the butt-end connectors for the older replacement and solder and shrinkwrap that one as well. He also soldered up the chafing third brake light wire.
Result? The brake lamp warning light is no longer shining in my face. For as long as I have owned my car, the left-side brake light seemed prone to making the warning lamp come on for one reason or another, while the right side has never given any problems. Usually in the past a new bulb would do the trick. But this time I think the cause of the problem has been addressed, rather than just the symptoms. I don't anticipate any more trouble with the brake light.
Bottom line? Examine the inside of your bulb sockets to make sure that all the metal contacts are intact, and examine the 3rd brake light wire where it goes from the car body to the left front corner of the trunk lid.