To the OP and everyone: please do write in to National Park Service and GGNRA requesting access to all fire roads and established trails in use and historically used by ranchers within these federal grazing areas. They are reviewing new management strategies for cattle management (and elk, and access) and allowing more park users to bike through cattle grazing is, in my educated opinion, low-hanging fruit that advocates, and locals, are asking for already to balance the current ranching equation. The ranchers in NPS are facing the facts that they don't share well with other users or animals. The environmental impact of bikes on the existing/historic ranch roads is very low to nil. Stay tuned for public comment period on the environmental document, but don't hesitate to contact NPS and GGNRA anyway as these public servants are working on it now.
That old road isn't maintained, and ends in a Park Residence. The driveways to Park Residences are specifically called out in the Superintendent's Compendium as one of the very few areas off limits to the public. Also, there's been a bit more enforcement in that area, so be wary of riding the unposted stuff. One of the Law Enforcement officers lives right there too. He's super nice, but don't ride into an easy bust.