I don't know the whole state of the vehicle. I don't want to. So I'll use PATCH. I know I want the horn to be in a honking state and remain in that state for 1 second. The implementation is responsible for doing what it needs to do in order to get the resource into the state (or differential state in this case) I told it to take.
I'm not usually in favor of nested API design, but complex resources like cars make sense, so:
My initial thought would be that a request for a "honk action" is not idempotent, so it should be a POST.
You could do it as a PUT or PATCH, but you'd have to do it differently from in your example in order to preserve idempotence, due to the complications of working with time.
Remember, if the request successfully goes through twice that should have the same effect as if only the first succeeded. One way to accomplish that would be to give an absolute start and end time for honk to be on. e.g.,
PUT /vehicles/{id}/horn { "enabled": true, "time_start": "2014-04-12T20:12:36.1", "time_end": "2014-04-12T20:12:36.6"}
I'm not usually in favor of nested API design, but complex resources like cars make sense, so:
PATCH /vehicles/{id}/horn { "enabled": true, "timeRemaining": 1000 }