As it turns out, an hour and a half after closing.
I went to the Joint Mathematics Meetings in San Francisco about two weeks ago. Since I was flying all the way to California anyway, I arranged to spend a few days at Disneyland first (of course). I stayed close to the park so I could walk in and out. (I discovered two years ago when the meetings were in San Diego and I visited Disneyland that this is a great way to visit. The whole resort is pretty walkable, even if I do end up with blisters on my blisters after a few days there.)
As it turns out, I stayed even closer to the park than I thought. I could see Space Mountain from my hotel room:
After the first night in the park, I left at closing and noticed when I got back to my room that I could still see Space Mountain. But at a later point, I looked out and it was gone. I eventually pinpointed the time on a later night: At an hour and a half after closing time, the mountain suddenly winks out of sight.
So I figure that must be when they turn off Disneyland.