Getting closer, thanks to Mike Muller.
Seems like my strip of breakers is made up of components kinda like this. There are several examples on line of different models: metal, plastic, with various brackets to hold it in place. In every case, there are two screw terminals, and what I assume is the reset button is on the end near the shorter brass terminal. These are from the Optifuse site.
My breakers are all in a nice row, with the short terminals facing in the same direction. And access to the ends where it seems likely the reset buttons are is blocked by a piece of plastic (?) which holds the whole thing in place.
Either the whole mishegas has to be disassembled, or (maybe!) I can slide a thin piece of plastic in there and manipulate the reset button without seeing what I'm doing or really knowing what I'm doing. Yeah, right.
Any bright ideas out there?