Based on information from the above links, and from "The Passes of Colorado" by the Helmuths, the pass appears to be at N37 54 23.39 W107 39 41.48. Rd 886 to the west (off of US-550) and Rds 20A and 11 to the east.
The Helmuths state, "Corkscrew Pass is accessible by 4WD on forest route #886. It divides the waters of Cement Creek to the east and Corkscrew Gulch to the west. The pass is named for Corkscrew Gulch on the west side of the pass and is located on the southwest flank of Red Mountain One, near the old mining town of Gladstone. It's a steep road to reach this pass, but the view from the top is well worth it. The pass is not named on forest service or topo maps; it is identified by local usage."