So... per the same GIS database that was consulted previously
(here it is again), not even actually. NPS jurisdiction is entirely limited to the section within the boundaries of Coronado National Monument (which makes sense). Between the east edge of the monument and AZ 92 it's Cochise County. Beyond the west edge of the monument (not the same point as the overlook, do note this) it is a NFS road, then part of it is Cochise County, then it flips back to NFS before reaching AZ 83.
That said I hesitate to slice up or ditch this one since it
does serve as a connection between AZ 83 (otherwise a system dead end) and AZ 92, and that is one of the explicit inclusion criteria:
1) a missing gap in an existing system (eg Mammoth Cave, California Routes, Yellowstone)
2) a specific NPS unit for the road (eg Natchez Trace, Blue Ridge, George Washington Memorial and Baltimore-Washington Parkways)
3) a through route linking roads already in (eg Painted Canyon Road)
4) an extension of an existing system into a park
5) roads that seem important enough and link with other roads - even if they dead-end
And unlike North and South Rim Drive in/around Canyon De Chelly which are both 100% BIA, at least
some of Montezuma Canyon Road is NPS maintained.
Likely leaving this one be.
