I called the Inyo National Forest's Wilderness Permit telephone number, 760-873-2483 and finally got through. I've called half a dozen times, and here's how it usually goes:
1. The line connects, you hear a recording, inviting you to press zero to speak to a live person.
2. Press zero, the line starts ringing. Ten rings, and it disconnects!
So that's the problem--there is no wait queue, no long-term hold system in place. I was told that there is no plan to change the disconnect.
All you can do is re-dial, press zero at the recording, hope that someone picks up in that first minute. Then repeat.