From what I have uncovered (not much) the mill near the NAPA store disappeared rather early.
There was another mill behind where the Branding Iron Motel is today. The location is occupied by the local rodeo grounds. The spur took off from the mainline very close to the current end of track and curved south. This track (or a portion of it) was still in place at the time of abandonment. I walked around the back side of the rodeo grounds once and found ties still in the ground. This track originally continued south as the Tierra Amarilla Southern. The time table location of the junction switch was known as "Biggs Junction"