I would get a copy of the blood results and look at them closely, for anything near the edges of the normal ranges. I have seen abnormal results that the vet has dismissed, many times on the forums and with my dogs
I would consider a tick panel, IFA titers, through protatek, but might be more interested in that having looked at the bloodwork.
My GSD used to shake his head like that. I am not sure what got rid of it, but I think that regular chiropractic care was one of the reasons that it went away: www.avcadoctors.com
Note that the dog's right eye does not appear to open as wide as the other.
After my experience with my boy, who had lifelong neck issues, and initially had that neck sway, I would start with a chiropractor and follow up with acupuncture.