The only neutral zone on earth I can remember was one on the boarder between Iraq and Saudi, the interesting thing was it wasn't along the entire boarder, just a sixty odd mile section out in the middle of the desert. Maybe the Klingon NZ isn't everywhere the two spaces touchs, just one spot.
That was the oval shape on the main viewer, the small KNZ.
There is also the DMZ between North and South Korea
In military terms, a demilitarized zone (DMZ) is an area, usually the frontier or boundary between two or more military powers (or alliances), where military activity is not permitted, usually by peace treaty, armistice, or other bilateral or multilateral agreement. Often the demilitarized zone lies upon a line of control and forms a de-facto international border.
Several demilitarized zones have also unintentionally become wildlife preserves, as they cause the land which they sit on to be too dangerous for construction and less exposed to human disturbance or hunting. See Korean Demilitarized Zone.
The Korean Demilitarized Zone is a strip of land running across the Korean Peninsula that serves as a buffer zone between North and South Korea. The DMZ cuts the Korean Peninsula roughly in half, crossing the 38th parallel on an angle, with the west end of the DMZ lying south of the parallel and the east end lying north of it. It is 155 miles (248 km) long and approximately 2.5 miles (4 km) wide, and is the most heavily militarized border in the world.
I read and reread the TWOK novelization countless times. If I remember correctly in the novel there are several Klingon ships, not just three. It's as if they keep coming and coming, overwhelming the Enterprise.