Teller County's GIS shows County Road 863 coming well short of what's mapped by the USGS by maybe a mile and doesn't give parcel owner information. The Fremont County GIS is even less helpful. I don't find publicly available GIS data via the Colorado GIS Coordination Office for either so there's only what's given on the county websites. Caltopo has parcel data. Looks like the county right of way or maintenance stops at the Strong Family property maybe?
There's routes in OpenStreetMap, which is likely the original source for other maps like Gaia or Garmin. I don't see any indication that the route has ever been verified in person for OSM. It was originally imported into the database from U.S. Census TIGER data about 14 years ago.
https://www.openstreetmap.org/way/17149776/history
https://www.openstreetmap.org/way/17047227/history
The USFS shows Beaver Creek State Wildlife Area that's adjacent along the creek up to Skagway Reservoir. Anyone fishing/hunting in the
BCSWA seem to be backpacking either from Skagway or a significant hike in following the creek from the south, so getting to that little spur is exceptionally difficult using the CPW guidelines.
Hard to say there's anything indicating an obvious, established legal route all the way but also nothing that would necessarily say it's definitely illegal to try following historical topo maps (e.g. pre-NEPA grandfathered routes which the USGS would have used for the National Map) or anything that's still on the ground. Neither the USFS MVUM (which isn't surprising, it's not USFS land) nor the BLM GTLF show anything. The BLM has much less developed travel data and generally a route on BLM land is open unless clearly closed via Carsonite sign or indicated on maps.
Your actual coordinates are on private property, that would be illegal to camp upon. But if there's a way to get in you might be OK on BLM dispersed or with a hunting or fishing license on the SWA property.
The USGS 7.5' quads.
Bull Mountain:
https://pdf.quad.download.s3.amazonaws.com/38105f1.pdf
Phantom Canyon:
https://pdf.quad.download.s3.amazonaws.com/38105e1.pdf
But even with more current data (talking around Mesa, Garfield, Rio Blanco, Moffat) I've personally come up to well and truly locked gates and fences where none are indicated on maps, thus forced backtracking.
Putting tires on dirt and eyes on things could be useful, too. This sort of exploration, to me, is *the* real essence of 4x4 and the relative security of driving a Toyota means you'll likely make it there and back.
Happy travels!