I've spotted that alignment too - it's an old old road that used to go all the way around from Placitas thru La Madera to Tijeras.    Can see in on this map, originally published in 1892 and reprinted in 1925:

The current Tecolote street in Placitas is on that old alignment.    I've looked for and spotted the segment your map shows; intersection with public road is now on a private lot; and behind (east) of that lot it enters the town of Tejon grant which the Diamond Tail Ranch seems to control access to now.   I've poked around the SE access too - there is a road from 14 thru town of Puertocito, past ghost town of Tejon (on the old map) to the Black Mesa Casino I'd driven a few years ago.  Blocked, last time I looked, by Diamond Tail gate west of Puertocito, about where public road drops north off Golden Open Spaces and connects with Puertocito road.

Neil McC