Not one to accept defeat, I figured it out. This picture is of the side of the removed connector, and the little "tab" on the back of the connector (that the green arrow is pointing to) is a catch which holds the connector from dropping down (and out). It must be depressed with a tiny screwdriver in the direction that the arrow is pointing. Some ham-handed previous owner did a lot of shade-tree work (and using that term is being kind), and it looks like there once was another tab on the other side.
Although I had the front fender liners off which facilitated getting a better look and seeing the solution, this can be accessed and removed by taking off the headlight and using a flashlight and inspection mirror to see what's back there.
Inasmuch as the reason I wanted to get better access to the wires going to that connector in order to wire in my side markers to flash with my turn signals, anyone wanting to do the same thing may want to remove the front fender liners as well.
