I think there is no way to apply the washer except manually. I'm like you, I couldn't find anything in the manual about the headlight wiper until I read about the windshield wipers. There it states something to the effect that when you have your windshield wipers at their fastest speed, the headlight wipers will come on and wipe the headlights a couple of times. So I think maybe there is no way to turn on just the headlight wipers and I sure didn't find anything about any auto-application of washer.
What I did was just spray some water on my headlights and then start my car and turn on the wipers to high. I then got out of the car and looked at my headlights. On the drivers' side the wiper was in a kind of locked down situation (it was under the little 'stop' on the bottom of the headlight) so it did not move. My passenger side headlight was partially up on the headlight. All I did was touch it and it made a swipe and then went down to 'off' position and then the noise shut up!
I found that to be completely amazing! I have suffered with my noise for a couple of months and all I had to do was touch the wiper to quiet it!
Good luck with your car- I hope it is fixed as easily as mine was.
