This is a simple spring loaded latch and when it's push in, it pops out. It may not pop out far enough, you'll have to determine that, but they are very cheap:
I would make wooden channel runners on the sides to keep it from falling down or getting cocked sideways. You can't use drawer slides because it needs to come all the way out, and they are typically screwed to the sides. A combination of drawer slides and a U channel could work, however.
Make the guides L shaped on each side of the cut out attached to the cabinet. Line the guides with laminate (formica) for the board to slide on. Route a finger pull on the bottom face of the cutting board. Place stops on the guides to prevent the board from going into the cabinet too far, allowing the board to stick out enough to grab the finger on the board. If you thing that a finger pull on the bottom of the cutting board may be hard to grab the board, a second way is to route a finger pull on each side edge (right/left) at the front and rear (in case the board is put in backwards). In either example the cutting board when inserted would stick out slightly.
As I wrote I already made 'L' (rabbeted) shape runners for the board to slide on and am considering lining the runner with a thin plastic/synthetic for to make it slide easier (and add wear resistance).
The measurement from outside of face frame to the back wall is 20".
The cutting board is 18" x 19".
I don't want the board to stand proud of the faceframe after it's inserted; I want it to be flush. The overhang of the counter top is only 1" and it will receive a windowsill profile on the edge which makes the actual overhang at the bottom edge
of the counter top just a fraction of an inch ... so the cutting board would project beyond the profiled counter edge and look weird, as if it's not pushed in all the way, and endlessly irk me.
There's only 1" of clearance between the cutting board end and the wall when it's inserted (no cabinet case back as it's a built in). So any plunger/spring hardware needs to be no longer than 1" long when retracted.
One other option is to widen the cutout groove in the face frame from 18-1/4" to 19-1/4" so that the cutting board stows with the longer dimension inserted. That still only leaves 2" of clearance at the wall for some sort of plunger mechanism. The faceframe is only 33" wide and the top rail is about 28"wide ... the width of the cutout already seems large and I'd prefer not to widen it further and diminish the structural integrity of the face frame.
Anyone know of a hardware item that would fit in those dimensions?
Or some other method of retrieval to pull the pull out?