If a person in the wilderness is reporting the emergency they should call 911 and explain they need search and rescue (SAR) for a remote emergency. Be prepared to identify the county you are in and nearest town.
If a family member needs to initiate a search and rescue or is reporting an overdue party, they should call the county sheriff office with jurisdiction for the area where the emergency is.
The Wilderness Permit Office staff can assist you with identifying which county or counties your trip is visiting. We can also provide the sheriff's phone number for the various Inyo trailheads. There is not just one sheriff's number to call because Inyo National Forest extends across multiple state and county jurisdictions.
Piute Pass trailhead is in Inyo County, California, Bishop area, and the phone for Sheriff SAR is 760-873-7887. If you cross over Piute Pass you are entering Fresno County. If you cross into Kings Canyon National Park, just south of Piute Pass, the park would have jurisdiction for SAR. Many trips will travel through several areas of jurisdiction. There is not a single website with all search and rescue contact information.
This is what i meant by standardization. How will my spouse know which county i'm in when i go missing? And I'm pretty sure my cell (which i don't carry in the backcountry) will be unreliable. They're still gonna have to wake up the permit station to try and figure out my itinerary.
I was impressed that they got back to me quickly, but still.