I have close to 30 plate holders of various makes as part of my collection of vintage English plate cameras. (Jim Galli accumulates lenses, I accumulate turn-of-the-century mahogany and brass stuff!)
If you could email me pictures of the camera back I can probably find a suitable holder for your camera from my pile of plate holders. I have a working idea of the configuration that you describe, and from what little information I can gather, you probably have a Houghton.
As to your question of how a plate holder stays in place: There are two ways, depending on the design of the back (this varies from maker to maker, and from one maker's model to the next.) If you take a look at your camera's back you will see "tracks" or grooves cut on the top and bottom edges. In some cameras, the holder is slipped into the tracks from the side. The tracks hold the holder in place after it is pushed completely to the left. From your description, your camera has a spring-loaded latch that locks the holder in place. This prevents the holder from being accidentally displaced as the holder darkslide is pulled for exposure. In other cameras, the holder is laid flat against the camera back, while aligning a tab on the holder with a cutout or notch on the camera back. The holder is then slid to the left along the camera back grooves.
I hope the answer helps. On another topic: it might be difficult to find correctly sized sheet film to put into half-plate holders unless you devise adaptors to hold 4x5 film in place, or cut 5x7 sheet film to fit. I have tried both in the past, and neither worked to my satisfaction. I tried it mostly just to find out how my plate cameras performed, and to find out if I could recreate that turn-of-the-century look. (I couldn't: emulsions on glass plates and modern film emulsions are two different things.)