I would make the clippers part of her life everyday until she gets used to them. The fact that she spooks/flinches when you turn them on and is consistently leaned away from them (if you look at how she's holding herself as you clip her muzzle, you'll notice that she leaned back away from them) tells me that she is, in fact, afraid of the clippers (probably the noise of them, since she seems fine when they aren't on). If I were working with her, I would have those clippers on, nearby, at all times while I worked with her until it's no big deal. Then, I would start having them on, near her muzzle, until she relaxes. Then I would turn them off and be done for the day. Once she's completely comfortable with them near her muzzle (ie, no leaning away from them, flinching when the noise comes on, etc) I'd repeat holding them, while on, near her bridle path and rubbing her bridle path with them until she relaxes a little, then I would stop for the day. I'd just keep doing that for as long as it takes for her to be fine (fine as in: no flinching, backing away, spooking, leaning away, etc) with them. It'll probably take a while, depending on how fast of a learner she is, but she obviously, from the video, is working her hardest to trust you, she's just a little worried.
I wouldn't try legitly clipping her bridle path until she's totally fine with the noise back there and the clippers being rubbed on her neck while they're running. I also think I'd leave the clippers on when I move them from her face back, that way she knows where they are and isn't surprised by a sudden loudish noise right by her ear, yknow? :)
Good luck! She's a super cute mare. :)
Fabio - 13 year old Arabian/Lipizzaner gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.